The potential function of a mono-stable system is studied in this paper. The response of pulse series with different half-peak width via the mono-stable system is analysed. Our conclusion is that the larger the half-peak width of the input pulse series, the higher the height of the output pulse series . Distortion of the pulse response wave appears. This is the reason that the potential function of the mono-stable system is similar to the horizontal line around zero point.#br#In view of the difficulties of adjusting parameter of the mono-stable system to reach stochastic resonance, a method of moving pulse series is put forward. Adjusting the system parameter is not considered but the stochastic resonance of the pulse signal is realized by setting an offset in the method. To reduce the response pulse wave distortion, a mechanism for the proposed method to reduce the distortion is discussed in detail. When noise exists, the mechanism reveals that the moving pulse series method can adjust the distribution of the noise power spectrum and improve the mono-stable stochastic resonance. Therefore, the method proposed in this paper is helpful to detect pulse signal masked by noise.