A ListBox is a control. You can't save a control as an application setting. What you can do is create an application setting of type StringCollection and bind that to the ListBox's DataSource property.
Have you created an application setting before? If not then I suggest that you do some reading on the subject first. If you have then just create another one but change the type to StringCollection. Now add you items in the Value field. Assuming that you have named your setting ListBoxItems you bind it to the ListBox like so: