Psáno narychlo v sobotu večer, tak to podle toho vypadá, ale funkční by to mohlo být

Imports System.IO

Public Class Form1

    Private Sub Button1_Click(sender As System.Object, e As System.EventArgs) Handles Button1.Click
        Dim drive As New DirectoryInfo("d:")

        Try
            For Each dir As DirectoryInfo In drive.GetDirectories
                Dim directories As New DirectoryInfo(dir.FullName)

                ListBox1.Items.Add(dir.Name)
                ListBox1.Refresh()
                Try
                    For Each subdir2 As DirectoryInfo In directories.GetDirectories
                        ListBox1.Items.Add(subdir2.Name)
                        ListBox1.Refresh()
                        Slozky(subdir2.FullName)
                    Next
                Catch ex As Exception

                End Try
            Next
        Catch ex As Exception

        End Try
    End Sub

    Private Sub Slozky(ByVal slozka As String)
        Dim directory As New DirectoryInfo(slozka)
        For Each dir As DirectoryInfo In directory.GetDirectories
            Dim directories As New DirectoryInfo(dir.FullName)

            ListBox1.Items.Add(dir.Name)
            ListBox1.Refresh()
            Try
                For Each subdir2 As DirectoryInfo In directories.GetDirectories
                    ListBox1.Items.Add(subdir2.Name)
                    ListBox1.Refresh()
                    Slozky(subdir2.FullName)
                Next
            Catch ex As Exception

            End Try
        Next
    End Sub
End Class