Abstract: An efficient and stable numerical method of differential-algebraic equations (DAEs) is one of the key problems in multi-body dynamics. For index 3 DAEs with a general mass matrix, a generalized-α-S method is presented after the deep study of implicit time-stepping methods introduced into multi-body dynamics. Based on the projection method of constraints, the generalized-α-S projection method is developed, which can keep the total energy of the system, the displacement constraints, as well as the velocity and acceleration constraints in higher degree of accuracy. With a longer time step, the method shows good stability to obtain higher computation efficiency.