Microwave curing technology, which has seen increased commercialization recently due to its ability to cut the curing time and ensure high quality, requires an understanding of the curing characteristics of composite materials of varying thickness. Therefore, this study aimed to perform cure monitoring to evaluate the effects of variations in thickness on the quality of microwave curing. For this study, a fiber Bragg grating sensor was used to measure temperature changes in specimens during the curing cycle for cure monitoring which is generally used for optimization of the curing cycle; then, the time taken for temperature increase and overshoot of the specimen, and the times at which the specimen thickness varied, were quantitatively evaluated. Testing confirmed that microwave curing reduced the curing time in the sections in which the temperature rose; also, the specimen thickness caused overshoot of up to approximately 40 °C at the side, which can affect the curing quality of the composite materials. Furthermore, voids were observed on the side of all specimens. The results indicated that, in order to improve the quality of microwave curing of composite materials, the curing cycle should be optimized by considering the characteristics of the microwave curing equipment.