In the MouseUp event handler, use HitTest to see what item is under the mouse and display an appropriate popup menu.

' Select the item right clicked.
Private Sub ListView1_MouseDown(Button As Integer, Shift As _
    Integer, x As Single, y As Single)
Dim item As ListItem

    If Button = vbRightButton Then
        Set item = ListView1.HitTest(x, y)
        If item Is Nothing Then
            Set item = ListView1.SelectedItem
            If Not item Is Nothing Then
                item.Selected = False
            End If
        Else
            Set ListView1.SelectedItem = item
        End If
    End If
End Sub

' Display the popup menu.
Private Sub ListView1_MouseUp(Button As Integer, Shift As _
    Integer, x As Single, y As Single)
Dim item As ListItem

    If Button = vbRightButton Then
        Set item = ListView1.HitTest(x, y)
        If item Is Nothing Then
            PopupMenu mnuPopupOffItem
        Else
            mnuPopupOnItemItemSelected.Caption = item.Text
            PopupMenu mnuPopupOnItem
        End If
    End If
End Sub