The effects of gauge transformation on Noether symmetry, Lie symmetry and Mei symmetry of a Birkhoff system are studied. Under certain conditions, the system can keep its Noether symmetry and conserved quantity. The Lie symmetry and Hojman conserved quantity of the system will still remain unchanged. The Mei symmetry and a new-type conserved quantity of the system may very, and the conditions under which the Mei symmetry and the new-type conserved quantity will remain are obtained. An example is given to illustrate the application of the results.