Aquí tienes otra manera parecida a la de seba123neo, pero sin borrar los items del ListBox:
Código:
Private Sub Command1_Click()
Dim s As String, a() As String, i As Integer
Open App.Path & "\Prueba.txt" For Input As #1
s = Input(LOF(1), #1)
Close #1
a = Split(s, vbNewLine)
List1.Clear
For i = 4 To UBound(a)
List1.AddItem a(i)
Next i
End Sub