In order to improve the weak signal processing capability of stochastic resonance (SR), a new asymmetric SR system with nonlinear jointed potential function is proposed in this paper. Firstly, the new joint potential stochastic resonance (JPSR) system is built by combined gaussian potential function and asymmetric bistable potential function. Secondly, the analytical expression of signal-to-noise ratio (SNR) is derived based on two-state theory and adiabatic approximation theory. Meanwhile, the influence of system parameters on SNR is discussed theoretically. Thirdly, by particle swarm optimization algorithm, the JPSR system is applied to detect actual bearing fault signals. Finally, according to numerial simulation, the results show that the proposed system can detect weak signal characteristics more effectively.