The Chebyshev polynomial approximation is applied to the dynamical response problem of stochastic Duffing-van der Pol system, with random parameters. The stochastic Duffing-van der Pol system is first reduced into an equivalent deterministic one for substitution, then the response of the stochastic Duffing-van der Pol system can be obtained by numerical methods for this equivalent deterministic system. Moreover, the symmetry-breaking bifurcation and period-doubling bifurcation of stochastic Duffing-van der Pol system are presented while the excitation frequency vary. Numerical simulation implies that the proposed method is a new effective approach to dynamical responses of stochastic nonlinear systems.