A periodic potential system excited by multi-low frequency weak signals, the high frequency signal and additive stable noise is constructed. Based on this model, the vibrational resonance phenomenon under stable noise is investigated by taking the mean signal-noise-ratio gain (MSNRI) of output as a performance index. Then the influences of stability index (0 2), the skewness parameter (-1 1) of stable noise, the amplification factor D and the high frequency signal amplitude B, and frequency on the resonant output effect are explored. The results show that under the different distributions of stable noise, the multi-low frequency weak signals detection can be realized by adjusting the high frequency signal parameter B or to induce vibrational resonance within a certain range. When (or ) is given different values, the curve of MSNRI-B has multiple peaks with the increase of B for a certain frequency , and the values of MSNRI corresponding to peaks of the curve of MSNRI-B are equal. So the intervals of B which can induce vibrational resonances are multiple, and the multiple resonance phenomenon turns periodic with the increase of B. Similarly, the curve of MSNRI- also has multiple peaks with the increase of for a certain amplitude B, so the intervals of which can induce vibrational resonances are also multiple. The difference is that the multiple resonance phenomenon becomes irregular with the increase of . Besides, the resonance intervals of B and do not change with nor . Under the different values of amplitude factor D, the resonance intervals of B (or ) do not change with the increase of D, indicating that only the energy of the high frequency signal transfers toward the signals to be measured, and the energy of stable noise does not transfer toward the signals to be measured. Besides, when B and are fixed, it can still be realized to detect the weak signal with the increase of D, which shows that the weak signal detection method based on vibrational resonance can overcome the shortcoming that noise intensity in industrial sites cannot be regulated and controlled. The results provide a new method of detecting the weak signal, and have potential application value in signal processing.