  This paper proposes a general symplectic Euler scheme for a class of
Hamiltonian stochastic differential equations driven by L$\acute{e}$vy noise in
the sense of Marcus form. The convergence of the symplectic Euler scheme for
this Hamiltonian stochastic differential equations is investigated. Realizable
numerical implementation of this scheme is also provided in details. Numerical
experiments are presented to illustrate the effectiveness and superiority of
the proposed method by the simulations of its orbits, symplectic structure and
Hamlitonian.
