Use the mciSendString API function to play mp3 files.
Here's code for a complete mp3 player.

Code:
Private Declare Function mciGetErrorString Lib "winmm.dll" Alias "mciGetErrorStringA" (ByVal dwError As Long, ByVal lpstrBuffer As String, ByVal uLength As Long) As Long
Private Declare Function GetShortPathName Lib "kernel32" Alias "GetShortPathNameA" (ByVal lpszLongPath As String, ByVal lpszShortPath As String, ByVal cchBuffer As Long) As Long
Private Declare Function mciSendString Lib "winmm.dll" Alias "mciSendStringA" (ByVal lpstrCommand As String, ByVal lpstrReturnString As String, ByVal uReturnLength As Long, ByVal hwndCallback As Long) As Long
Private Declare Function SendMessage Lib "user32" Alias "SendMessageA" (ByVal hwnd As Long, ByVal wMsg As Long, ByVal wParam As Long, lParam As Any) As Long
Private Declare Function ReleaseCapture Lib "user32" () As Long
Private Declare Function SetWindowPos Lib "user32" (ByVal hwnd As Long, ByVal hWndInsertAfter As Long, ByVal x As Long, ByVal y As Long, ByVal cx As Long, ByVal cy As Long, ByVal wFlags As Long) As Long
Private Const SWP_NOMOVE = &H2
Private Const SWP_NOSIZE = &H1
Private Const HWND_TOPMOST = -1
Private Const HWND_NOTOPMOST = -2
Private TheFileName As String



Private Function IsItPlaying() As Boolean
Static yn As String * 30
    mciSendString "status MP3Play mode", yn, Len(yn), 0
    IsItPlaying = (Mid$(yn, 1, 7) = "playing")
End Function

Private Function mp3Play(FileName As String)
Dim cmdToDo As String * 255
Dim dwReturn As Long
Dim ret As String * 128

Dim tmp As String * 255
Dim lenShort As Long
Dim ShortPathAndFie As String
    
    If Dir(FileName) = "" Then
        mmOpen = "Error with input file"
        Exit Function
    End If
    lenShort = GetShortPathName(FileName, tmp, 255)
    ShortPathAndFie = Left$(tmp, lenShort)
    glo_hWnd = hwnd
    cmdToDo = "open " & ShortPathAndFie & " type MPEGVideo Alias MP3Play"
    dwReturn = mciSendString(cmdToDo, 0&, 0&, 0&)

    If dwReturn <> 0 Then  'not success
        mciGetErrorString dwReturn, ret, 128
        mmOpen = ret
        MsgBox ret, vbCritical
        Exit Function
    End If
    
    mmOpen = "Success"
    mciSendString "play MP3Play", 0, 0, 0
End Function

Private Function mp3Pause()
    mciSendString "pause MP3Play", 0, 0, 0
End Function

Private Function mp3Unpause()
    mciSendString "resume MP3Play", 0, 0, 0
End Function

Private Function mp3Stop() As String
    mciSendString "stop MP3Play", 0, 0, 0
    mciSendString "close MP3Play", 0, 0, 0
End Function

Private Function PositionInSec()
Static PIS As String * 30
    mciSendString "set MP3Play time format milliseconds", 0, 0, 0
    mciSendString "status MP3Play position", PIS, Len(PIS), 0
    PositionInSec = Round(Mid$(PIS, 1, Len(PIS)) / 1000)
End Function

Private Function Position()
Static P As String * 30
    mciSendString "set MP3Play time format milliseconds", 0, 0, 0
    mciSendString "status MP3Play position", P, Len(P), 0
    sec = Round(Mid$(P, 1, Len(P)) / 1000)
    If sec < 60 Then Position = "0:" & Format(sec, "00")
    If sec > 59 Then
        mins = Int(sec / 60)
        sec = sec - (mins * 60)
        Position = Format(mins, "00") & ":" & Format(sec, "00")
    End If
End Function

Private Function LengthInSec()
Static L As String * 30
    mciSendString "set MP3Play time format milliseconds", 0, 0, 0
    mciSendString "status MP3Play length", L, Len(s), 0
    LengthInSec = Round(Val(Mid$(L, 1, Len(L))) / 1000) 'Round(CInt(Mid$(s, 1, Len(s))) / 1000)
End Function

Private Function Length()
Static L As String * 30
    mciSendString "set MP3Play time format milliseconds", 0, 0, 0
    mciSendString "status MP3Play length", L, Len(L), 0
    sec = Round(Val(Mid$(L, 1, Len(L))) / 1000) 'Round(CInt(Mid$(l, 1, Len(l))) / 1000)
    If sec < 60 Then Length = "0:" & Format(sec, "00")
    If sec > 59 Then
        mins = Int(sec / 60)
        sec = sec - (mins * 60)
        Length = Format(mins, "00") & ":" & Format(sec, "00")
    End If
End Function

Private Function TimeRemaining() As String
    RSecs = (LengthInSeconds) - (PositionInSec)
    RMins = Int(RSecs / 60)
    RSecs = Format((((RSecs / 60) - RMins) / 1.67), "0.00") * 100
    If RSecs > 59 Then
        RMins = RMins + 1
        RSecs = 0#
    Else: RMins = RMins
        RSecs = RSecs
    End If
    If RSecs < 10 Then
        TimeRemaining = RMins & ":0" & RSecs
    Else: TimeRemaining = RMins & ":" & RSecs
    End If
End Function

Private Function SeekTo(Second)
    mciSendString "set MP3Play time format milliseconds", 0, 0, 0
    If IsItPlaying = True Then mciSendString "play MP3Play from " & Second, 0, 0, 0
    If IsItPlaying = False Then mciSendString "seek MP3Play to " & Second, 0, 0, 0
End Function

Private Function FastFoward(Second)
    Second = (PositionInSec + Second) * 1000
    mciSendString "set mpeg time format milliseconds", 0&, 0&, 0&
    If IsItPlaying = True Then
        mciSendString "play mpeg from " & Second, 0&, 0&, 0&
    Else: mciSendString "seek mpeg from " & Second, 0&, 0&, 0&
    End If
End Function

Private Function Rewind(Second)
    Second = (PositionInSec - Second) * 1000
    mciSendString "set mpeg time format milliseconds", 0&, 0&, 0&
    If IsItPlaying = True Then
        mciSendString "play mpeg from " & Second, 0&, 0&, 0&
    Else: mciSendString "seek mpeg from " & Second, 0&, 0&, 0&
    End If
End Function

Private Function SetVolume(Channel As String, VolumeValue As Long) As String
Dim cmdToDo As String * 128
Dim dwReturn As Long
Dim ret As String * 128
Dim VolumeV As Long
VolumeV = VolumeValue

If VolumeV < 0 Or VolumeV > 100 Then
    SetVolume = "out of volume"
    Exit Function
End If

VolumeV = VolumeV * 10

If LCase(Channel) = "left" Or LCase(Channel) = "right" Then
    cmdToDo = "setaudio mpeg " & Channel & " Volume to " & VolumeV
Else
    cmdToDo = "setaudio mpeg Volume to " & VolumeV
End If

dwReturn = mciSendString(cmdToDo, 0&, 0&, 0&)

If Not dwReturn = 0 Then  'not success
    mciGetErrorString dwReturn, ret, 128 'Get the error
    SetVolume = ret
    Exit Function
End If

'Success
SetVolume = "Success"
End Function

Private Function Pitch(Value As Integer) As String
    Dim dwReturn As Long
    Dim ret As String * 128
    Dim Pval As Long
    Value = Value - 100
    Pval = 1000 + Value
    dwReturn = mciSendString("set mpeg speed " & Pval, 0&, 0&, 0&)
    If Not dwReturn = 0 Then  'not success
        mciGetErrorString dwReturn, ret, 128 'Get the error
        Pitch = ret
        Exit Function
    End If
    
Pitch = "Success"
End Function