In the present article, a one-dimensional dynamic thermoelastic problem in a functionally graded material (FGM) thin film subjected to a thermal shock loading is analyzed. An exact analytical solution is obtained by employing techniques of the space-variable transformation and Laplace transform, in the case where variations in material properties of the FGM thin film are expressed as exponential functions of the space-variable. Numerical calculations for time histories of thermal stresses have been carried out. Obtained numerical results reveal that the thermal stress oscillation is unsteady when the mechanical impedance depends on the space-variable, whereas it is monotonic and periodic when the impedance is independent of the space-variable. The factor which causes the different behavior of the thermal stress oscillations is also investigated based on the analytical and numerical results.