In this paper we combine stable noise with bistable stochastic resonance to investigate the parameter-induced stochastic resonance in the high-and low-frequency (both for multi-frequency) weak signal detection with different stable noise, and explore the action laws between the stability index (0 2) and skewness parameter (-1 1) of stable noise, and the resonance system parameters a, b on the resonant output effect. Results show that for different distribution of stable noise, the high- and low-frequency weak signal detection can be realized by tuning the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with or . Moreover, while detecting the high- and low-frequency weak signal, the action laws of the resonant output effect which are affected by or are the same. These results will contribute to realize a reasonable selection of parameter-induced stochastic resonance system parameters under stable noise, and lay the foundation for a practical engineering application of multi-frequency weak signal detection based on the stochastic resonance.