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The strong convergence of the semi-implicit Euler-Maruyama (EM) method forstochastic differential equations with non-linear coefficients driven by aclass of L\'evy processes is investigated. The dependence of the convergenceorder of the numerical scheme on the parameters of the class of L\'evyprocesses is discovered, which is different from existing results. In addition,the existence and uniqueness of numerical invariant measure of thesemi-implicit EM method is studied and its convergence to the underlyinginvariant measure is also proved. Numerical examples are provided to confirmour theoretical results.

The semi-implicit Euler-Maruyama method for nonlinear non-autonomous stochastic differential equations driven by a class of L\'evy processes