This paper analyzes the crack initiation and fatigue propagation at the edge of a dilution hole in combustor's liner at high temperature. A plane model with a crack at the edge of a round hole is built at high temperature and under anisothermal condition, and the numerical simulations via finite element method at stable temperature and transient temperature are performed respectively. Furthermore, the comparison between evaluations of stress intensity at crack tip respectively by J- integral and C (t) - integral is made. According to the analysis, it is found that there is evident difference between the results J - integral and C (t) integral under the conditions of stable and transient temperature. This phenomenon is tentatively discussed for the judgment of the crack fatigue propagation.