Aviation aircraft will be subjected to a large number of complex random vibration loads during service, and its structure is prone to vibration fatigue, which leads to damage or even failure, causing serious losses. The vibration fatigue test and theoretical analysis are carried out on a typical cantilever beam as an object ,the SIF solution method for cracked beams under random vibration loading is investigated, and a time-domain method based on Hudson"s theory is proposed to estimate the vibration fatigue crack growth life by combining with the Paris formula. It is found that the time-domain method proposed based on the Hudson method compares well with the experimental estimation results, which verifies that the model can effectively describe the random vibration crack growth behavior.