This paper shows the Fokker-Planck(FP) equation of a stochastic system with double singularities driven by Gaussian colored noise. Based on the FP equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The relationship between the properties of double singularities, noise correlation time and dissipative parameter and their effects on entropy flux and entropy production are discussed.