The　implicit　methods　on　Lie　group　are　developed　for　multibody　system　dynamics.　To　avoid　the　violation　of　the　displacement,　velocity　and　acceleration　constraints　of　the　nonlinear　differential-algebraic　equations,　the　constraint-stabilized　equations　on　Lie　group　are　formulated.　The　implicit　method　for　the　Euler-Lagrange　equations　and　the　symplectic　Euler　method　for　the　constrained　Hamilton　equations　are　presented.　These　methods　can　keep　the　stability　of　the　displacement,　velocity　and　acceleration　constraints　at　the　same　time　during　the　longer　simulation.　A　three-dimensional　single　pendulum　and　a　three-dimensional　double　pendulum　are　used　to　verify　the　accuracy　of　the　constraint-stabilized　Euler　methods　on　Lie　group　and　the　orthogonality　preservation　of　the　rotation　matrix.