For the high-order Maggi equation of nonholonomic systems, when it meets certain conditions,the Maggi equation can be transformed into a Birkhoffian system.By constructing the generating function, the system is investigated numerically using the symplectic geometric algorithm of the Birkhoffian system.Compared with the above-mentioned algorithm with the classical Runge-Kutta method, Birkhoffian symplectic scheme is very accurate in a long-term tracing.