Abstract: The phenomenon of stochastic resonance in an RC series circuit, whose time constant is fluctuated by asymmetric dichotomous noise, is investigated. Based on the random average method and Shapiro-Loginov formula, An explicit expression of the Output Amplitude Gain (OAG) is obtained. The results show that the OAG is a non-monotonic function of strength, correlation rate, and asymmetry of the noise. The minimum of OAG can be obtained by choosing appropriate values of the parameters of both noise and system. The minimum of the function of OAG as asymmetry or correlation rate of noise are not varied with signal frequency.