Constraints stabilization method on Lie group is studied for different?algebraic equations (DAEs) of multibody system dynamics. Considering the displacement constraints, the velocity constraints and the acceleration constraints equations, the new Lagrange multipliers are used to construct the new DAEs on Lie groups. Then, using the ward difference method and CG ( Crouch?Grossman) method, high accuracy simulation results is obtained by solving the constraints stabilization DAEs. The constraints stabilization method can accurately maintain the constraint equation at all levels, and can maintain the orthogonality of rotation matrix. Meanwhile, the total energy error of the system is smaller.