Установили:
ListView0.OLEDropMode = vbOLEDropManual
и на событие OLEDragDrop:
Private Sub ListView0_OLEDragDrop(Data As Object, Effect As Long, _
Button As Integer, Shift As Integer, x As Single, y As Single)
Dim i As Long
If TypeName(Data) = "IVBDataObject" Then
For i = 1 To Data.Files.Count
Debug.Print Data.Files(i)
Next
End If
End Sub