  A class of Hamiltonian stochastic differential equations with multiplicative
L\'{e}vy noise in the sense of Marcus, and the construction and numerical
implementation methods of symplectic Euler scheme, are considered. A general
symplectic Euler scheme for this kind of Hamiltonian stochastic differential
equations is devised, and its convergence theorem is proved. The second part
presents realizable numerical implementation methods for this scheme in
details. Some numerical experiments are conducted to demonstrate the
effectiveness and superiority of the proposed method by the simulations of its
orbits, Hamlitonian,and convergence order over a long time interval.
