In calculating random fatigue life of structures in engineering at present, the stress life method based on the axial tension-compression fatigue life S-N(stress-number of cycles) curve is often used. Easy as it is to use, it often ignores not only the single-axis S-N curve, causing inaccurate reflection of the effect of multi-axial stress state, but also the resonance on the structure fatigue life in random vibration, as a result, the method in the prediction of fatigue life of structures under random vibration with actual life tends to have a larger error. The triaxial factor was introduced to reflect the multi-axial stress state of the structure under random vibration, and its expression in frequency domain was generalized. Based on this, the multi-axial vibration factor, a new random vibration fatigue damage parameter, was proposed. The new damage parameter not only considers the effect of multi-axial stress state and resonance on fatigue life under random vibration of the structure, but also has a simple form for engineering application. By using the new random vibration fatigue damage parameters, the multi-axis S-N curve for random vibration was obtained, and a new random vibration fatigue life prediction method was established. By predicting the random vibration fatigue life of 7075-T6 and LY12CZ aluminum alloy notch specimen, the results show that the method can accurately predict the fatigue life of two kinds of notch specimens under random vibration.