The stochastic resonance of a RLC series resonant circuit whose capacitance parameters and excitation signal were disturbed by Gaussian white noise was studied using Fourth-order Runge-Kutta algorithm, and taking signal to noise ratio(SNR) gain and spectral power magnification as indicators for stochastic resonance(SR) measurements. The results showed that it an underdamped RLC series resonant circuit has appropriate system parameters, noise parameters and excitation signal frequencies, its SNR gain and spectral power magnification are non-monotonic functions of noise intensity and frequency of input signal, and their values are greater than 1, stochastic resonances occur in the circuit; while in critical damping or overdamped case, although the SNR gain under a certain condition is also non-monotonic function of noise intensity and input signal frequency, the spectral power magnification value is less than 1; the occurrence of stochastic resonance improves SNR, but signal energy is not enhanced. This conclusion made application of an underdamped RLC series resonant circuit in weak signal detection possible.