In recent years, the increase in gas turbine inlet temperatures has led to the problem of excessive temperatures in gas turbine blades. To address this issue, thermal barrier coatings (TBCs), internal cooling, and film cooling have been applied to the hot-side surfaces of the blades. However, it remains necessary to manage crack initiation and spalling damage of the TBC caused by thermal fatigue around the cooling holes. In this study, a thermomechanical fatigue analysis was performed on a TBC/IN738LC plate-type substrate with cooling holes using finite element analysis software. The analysis incorporated a damage-coupled inelastic constitutive equation for TBC developed by our research group. The damage and thermal stress fields around the cooling holes under cyclic loading were analyzed under thermomechanical fatigue conditions, considering both in-phase conditions—where the temperature and load patterns were synchronized—and out-of-phase conditions, where they were out of sync. Under temperature and cyclic loading conditions where the mechanical stress level around the cooling holes was lower than the thermal stress, thermal fatigue cracks were initiated at the edges of the cooling hole, notably at the 3 and 9 o’clock positions, corresponding to the loading direction, and the cracks propagated near the top coating (TC)/substrate interface. Conversely, under loading conditions where the mechanical stress exceeded the thermal stress, thermal fatigue cracks initiated at the edges of the cooling hole at 6 and 12 o’clock positions, and the cracks propagated rapidly near the TC surface. The stress level was higher in the out-of-phase condition than in the in-phase condition, and the fatigue crack initiation life was shorter. However, the differences in the temperature loading patterns had little effect on the crack initiation location.