We propose a new piecewise-linear model. The principle of stochastic resonance in the new piecewise-linear model is introduced, and the formula of the signal-to-noise ratio (SNR) is deduced. It is proved that stochastic resonance characteristics can be utilized to realize the conversion of noise energy into periodic signal energy. The results clearly show the enhancement of the SNR of the output signal. The model characteristic that the weak periodic signal can be detected from noise background is investigated by the numerical simulation. The stochastic resonance system based on the model is built by using a circuit. The behaviors of stochastic resonance are studied when the circuit is driven by noise and period signal. The simulation and experimental results show that the model can effectively detect weak periodic signal, and enhance the SNR prominently.