You need to read back the value of the variable and compare it with the items in the list, then set the list index. e.g.
Code:
Option Explicit
Private oVars As Variables
Private oVar As Variable
Private i As Long
Private Sub UserForm_Initialize()
Dim listEntries1(3, 1) As Variant
Set oVars = ActiveDocument.Variables
With Me
.ComboBox1.ColumnCount = 2
.ComboBox1.ColumnWidths = "50;20"
listEntries1(0, 0) = "This"
listEntries1(0, 1) = 1
listEntries1(1, 0) = "is"
listEntries1(1, 1) = 2
listEntries1(2, 0) = "a"
listEntries1(2, 1) = 3
listEntries1(3, 0) = "Test"
listEntries1(3, 1) = 4
.ComboBox1.List = listEntries1
.ComboBox1 = ComboBox1.List(0)
'Read back the value of the variable (if present)
For Each oVar In oVars
If oVar.Name = "var1" Then
For i = 0 To .ComboBox1.ListCount - 1
'Compare the value with the list items
If Trim(.ComboBox1.List(i)) = Trim(oVar.Value) Then
'Set the listindex to the value of i
.ComboBox1.ListIndex = i
Exit For
End If
Next i
Exit For
End If
Next oVar
End With
End Sub