Using the complex function and the image method, thermal wave scattering in the slab of functionally graded materials with a cylindrical subsurface inclusion was investigated. Based on the Non-Fourier’s heat conduction equation, the temperature field in the slab of FGM with a cylindrical subsurface inclusion was analyzed. The analytical solution of the scattered field of thermal waves in the slab of FGM was obtained. The temperature wave is excited at the surface of FGM by the periodically modulated beam. The upper and lower temperatures are the environmental temperature. The influence of the geometrical and thermophysical parameters of the cylindrical inclusion on the temperature at the frontal surface of FGM was calculated. The results of this paper are expected to provide calculation methods and reference data for infrared thermal wave nondestructive testing of functionally graded materials.