In view of the random impulse of the mechanical environment noise and the shortcoming of traditional measurement index for recognizing the impact signal of the mechanical fault, a new criterion (Kurtosis-Intercorrelation combined index, abbreviated as KI) using as the basis for detecting the impact signal, which is constructed with kurtosis index and cross correlation coefficient, is proposed, and the detection of impact signal in asymmetric bistable system is studied with utilizing Levy noise as background noise. Firstly, the transition density function of particles and the construction method of KI in asymmetric bistable system driven by Levy noise are theoretically analyzed. Secondly, the variation trend of the output KI value of the system with the system parameter a and the asymmetric factor C is studied respectively, when the Levy noise characteristic index αis 1.5. Finally, the method is applied to the detection of the actual mechanical fault impact signal. The results of simulation and experiment show that, compared with the kurtosis index as an impact signal detection basis, KI can increase the signal characteristic amplitude of the output of the system more than one times. The output KI value of the system increases with the C first and then decreases. When the asymmetric factor C is 0.54, the output KI value of the system is increased by 7.02% than that of when C is 0. The engineering example data proves that the method can extract the time-domain and frequency domain feature information of fault signal effectively, and it can be applied to the actual mechanical fault detection.