add:
Exit Sub

see below what i modified your code:
Sub Macro1()
Dim Thyag
On Error GoTo Thyagaraj_Not_Found

Cells.Find(What:="Thyagaraj", After:=ActiveCell,
LookIn:=xlFormulas, LookAt _
:=xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext,
MatchCase:= _
False).Activate

With Selection.Interior
.ColorIndex = 6
.Pattern = xlSolid
exit sub

Thyagaraj_Not_Found:

'Selection.Font.Bold = True
Thyag = MsgBox("Thyagaraj not found")
End With
End Sub


"Thyagaraj" wrote:

Dear Friends,

In the code given below if there is no error then also the msg box is
displayed.

Any help please.

Sub Macro1()
Dim Thyag
On Error GoTo Thyagaraj_Not_Found

Cells.Find(What:="Thyagaraj", After:=ActiveCell,
LookIn:=xlFormulas, LookAt _
:=xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext,
MatchCase:= _
False).Activate

With Selection.Interior
.ColorIndex = 6
.Pattern = xlSolid


Thyagaraj_Not_Found:

'Selection.Font.Bold = True
Thyag = MsgBox("Thyagaraj not found")
End With
End Sub


Thanks in Advance

Thyagaraj