For the difficulties of classical bi-stable stochastic resonance (CBSR) system in amplification and detection of weak signals, an underdamped exponential tri-stable stochastic resonance (UETSR) system in a Levy noise background is proposed. The UETSR system is constructed by combining the bi-stable potential and exponential potential function, and using the property that non-Gaussian noise can effectively improve the signal-to-noise ratio. Firstly, the steady-state probability density function of the system is derived. The mean signal-to-noise ratio improvement (MSNRI) is adopted as an index to measure the stochastic resonance performance. The quantum particle swarm algorithm is used on parameters optimization. The effect of each parameter of the system on the output variation pattern of the UETSR system with different parameters α and β of Levy noise is investigated. Finally, the UETSR, CBSR and classical tri-stable stochastic resonance system (CTSR) are applied to the bearing fault diagnosis, and the amplitudes at the inner and outer ring fault frequencies after the system output increased by 197. 58, 1. 153, 18. 81 and 238. 87, 26. 63, 39. 72, respectively, compared to the input signal. The spectral level ratios of the highest peak to the second highest peak were 5. 44, 4. 03, 3. 85 and 5. 10, 3. 79, 5. 05. The experimental results show that SR phenomena can be induced by different system parameters, and the UETSR system outperformed the CBSR system and the CTSR system. The above conclusions prove that the system has excellent performance and strong practical significance