Based on the method of transformation, this paper studies the Fokker-Planck equation of a stochastic system with double singularities driven by aussian colored noise. According to the definition of Shannon's information entropy and the Schwartz inequality principle, the explicit time dependence of the upper bound of the rate of entropy change is obtained for the first time. The relationship between the properties of double singularities, noise correlation time and dissipative parameter and their effect on the upper bound of the rate of entropy change are discussed.