A simple method using semaphore class(creating object to satisfy one request) in Application Startup's event(Go to Project Properties, Application Tab, View Application Events).  


Partial Friend Class MyApplication
        Dim AmINew As Boolean
        Dim sp As New System.Threading.Semaphore(0, 1, "MyUniqueApplicationName", AmINew)
        Private Sub CheckingPrevInstance(ByVal s As Object, ByVal e As ApplicationServices.StartupEventArgs) Handles Me.Startup
            If AmINew Then
                MessageBox.Show("Yes")
            Else
                MessageBox.Show("I cannot co-exist ")
                e.Cancel = True
            End If
        End Sub
    End Class