It is improper to use frequency domain signal-to-noise ratio as a measure to judge whether stochastic resonance happens with chirp signal which is common in engineering. As a result, there is little literature on this subject. Using the energy aggregation in an optimal fractional Fourier transform domain of chirp signal, in this paper we propose a new signal-to-noise ratio defined in an optimal fractional domain to study the stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise. A new phenomenon is found, that is, the stochastic resonance phenomenon weakens gradually as the frequency of chirp signal increases. And it is reasonably explained in this paper. The consistency of simulation results with theoretical analysis verifies the effectiveness of the method proposed in this paper.