Private Sub ListView1_ColumnClick( _
    ByVal ColumnHeader As MSComctlLib.ColumnHeader)
   
  'lvwAscending ' orden ascendente
  'lvwDescending ' orden descendente
 
  With ListView1
       If .SortOrder = lvwAscending Then
          .SortOrder = lvwDescending
       Else
          .SortOrder = lvwAscending
       End If
       
       .Sorted = True
       ' columna por la cual se ordena
       '( en este caso hay una sola )
       .SortKey = 0
  End With
End Sub

Private Sub ListView1_ColumnClick( _
    ByVal ColumnHeader As MSComctlLib.ColumnHeader)
 
Select Case ColumnHeader.Index
 
Case 1
 
With listview
If .SortOrder = lvwAscending Then
.SortOrder = lvwDescending
Else
.SortOrder = lvwAscending
End If
.SortKey = ColumnHeader.Index - 1
.Sorted = True
End With
 
Case 2

With listview
If .SortOrder = lvwAscending Then
.SortOrder = lvwDescending
Else
.SortOrder = lvwAscending
End If
.SortKey = ColumnHeader.Index - 1
.Sorted = True

Case 3

 With listview
If .SortOrder = lvwAscending Then
.SortOrder = lvwDescending
Else
.SortOrder = lvwAscending
End If
.SortKey = ColumnHeader.Index - 1
.Sorted = True

End Select

End Sub