The Pfaff-Birkhoff principle and the Birkhoff equations for relativistic Birkhoff systems are given. The definition of an infinitesimal generator for the relativistic Birkhoff systems is given; by using the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the systems are established; the structure equation and the conserved quantities are obtained. And the inverse problem of Lie symmetries of the systems is also studied. Two examples are given to illustrate the application of the result.