In this paper, the Levy noise is combined with a power function type monostable stochastic resonance system for the first time. In order to ensure the reliability of the experimental data, the average signal-to-noise ratio gain is regarded as an index to investigate the stochastic resonance phenomenon stimulated by Levy noise. Potential function form of the monostable system and the method of generating Levy noise are presented in detail. The pulse characteristic and smear characteristic of Levy noise are also presented in detail. The laws for the resonant output of monostable system, governed by parameters a and b, the intensity amplification factor D of Levy noise, are explored under different values of characteristic index and symmetry parameter of Levy noise. Results show that no matter whether it is under any different characteristic index or symmetry parameter of Levy noise, the weak signal can be detected by adjusting the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with nor . Moreover, the same rule is founded which by adjusting the intensity amplification factor D of Levy noise can also realize synergistic effect when studying the noise-induced stochastic resonance, and the interval of D does not change with nor ; the best value of characteristic index is =1 under any system parameter, and the best value of symmetry parameter is =1 under any system parameter. So, the system performance is best when =1 and =1. Finally, the interaction relationship between system parameters a and b is investigated, and it is found that the interval of a or b will change with b or a when characteristic index , symmetry parameter and the intensity amplification factor D of Levy noise are fixed. These results will contribute to reasonably choosing the system parameters and intensity amplification factor of power function type monostable stochastic resonance system under Levy noise, and provide a reliable basis for practical engineering application of weak signal detection by stochastic resonance.