This paper investigates the influences of nonzero mean Poisson impulse amplitudes on the response statistics of dynamical systems. New correction terms of the extended Itô calculus, as a generalization of the Wong–Zakai correction terms in the case of normal excitations, are adopted to consider the non-normal property in the case of Poisson process. Due to these new correction terms, the corresponding drift and diffusion coefficients of Fokker–Planck–Kolmogorov (FPK) equation have to be modified and they become more complicated. Herein, the exponential–polynomial closure (EPC) method is employed to solve such a complex FPK equation. Since there are no exact solutions, the efficiency of the EPC method is numerically evaluated by the simulation results. Three examples of different excitation patterns are considered. Numerical results indicate that the influence of nonzero mean impulse amplitudes on system responses depends on the excitation patterns. It is negligible in the case of parametric excitation on displacement. On the contrary, the influence becomes significant in the cases of external excitation and parametric excitation on velocity.