Abstract: This paper applied a non-Gaussian moment equation closure method to compute random responses of a two-degree-of-system with strongly nonlinear coupling under parametric excitation. After removing the coupling of interia in the motion equations of the system by using successive elimination technique, the 69 moment equations have been derived and integrated by RK4 combined with central cumulate truncation scheme. A comparison of the results by different numerical methods in also given in this paper.