A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the rate of entropy change of the system is calculated in the presence of a non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant γ, parameter q, and noise correlation time τ on the upper bound for the rate of entropy change.