This paper focuses on studying the relation between the Mei symmetry and the Noether symmetry, takes the Birkhoff system as a example. The variational problem for Birkhoffian and Birkhoff′s functions under action of infinitesimal generator vectors is studied. The Birkhoff′s equations for the variational problem are established. The Noether symmetry for the variational problem is studied and corresponding conserved quantity is given. The studies show that the Birkhoff equations the Noether identity and the Noether conserved quantity of the variational problem are exactly the same with the criterion equation and structural equation and the conserved quantity for Mei symmetry of classical Birkhoff system. In the end of the paper, we take the wellknown Emden equation as example to illustrate the application of the results.