the closing event is triggered when the form is already being closed so I don't think that using me .close will have any effect in your program.
I would suggest that you put that code inside a button event instead of closing event of the form.

vb Code:
  1. private sub button1_click()sender as object, e as eventArgs) Handles button1.click
  2.  
  3. If MessageBox.Show("Do you want to exit application completely?", "Quit Form", MessageBoxButtons.YesNo, MessageBoxIcon.Question) = Windows.Forms.DialogResult.Yes Then
  4.             'do nothing
  5.             Application.Exit()
  6.         Else
  7.             'e.Cancel = True
  8.             Me.Close()
  9.         End If
  10. end sub