Suspiciously redundant Excel macro code
Not relevant to your algo, but you shouldn't be using "" like this; use the vbNullString language constant instead, which consumes 0 memory (as opposed to "" which has the overhead of a string).

As for suggestions, in order to find a better way to do something, it's important to first understand what's going on. And proper indentation greatly helps for that:

CurMonth = target.Offset(5 - target.Row).Value
If CurMonth = vbNullString Then
    CurMonth = target.Offset((5 - target.Row), -1).Value
    If CurMonth = vbNullString Then
        CurMonth = target.Offset((5 - target.Row), -2).Value
        If CurMonth = vbNullString Then
            CurMonth = target.Offset((5 - target.Row), -3).Value
        End If
    End If
End If
Debug.Print CurMonth


Something sticks out right away - every new nested level seems to increment the offset, so what you really have is this:

CurMonth = target.Offset((5 - target.Row), n).Value
If CurMonth = vbNullString Then
    n = n - 1
    [and do that again while n &gt; -3]


This looks like a recursive logic - something like this:

Private Function GetCurMonth(ByVal n As Long) As String
    Dim result As String

    result = target.Offset((5 - target.Row), n).Value
    If result = vbNullString And n &gt; -3 Then
        n = n - 1
        result = GetCurMonth(n) 'recursive call
    End If

    GetCurMonth = result
End Sub


Also CurMonth has no reason not to be called CurrentMonth I guess. As Comintern mentioned, it would be easier to give a better review with more [code] context.