This study investigates three-dimensional thermal residual stresses occurring in an adhesively-bonded functionally graded single-lap joint subjected to a uniform cooling. The adherends are composed of a through-the-thickness functionally graded region between Al2O3 ceramic and Ni metal layers. Their mechanical properties were calculated using a power law for the volume fraction of the metal phase and a 3D layered finite element was implemented. In a free single-lap joint the normal stress sigma(xx) was dominant through the overlap region of the upper and lower adherends and along the adhesive free edges, whereas the transverse shear stress sigma(xy) concentrations appeared only along the free edges. The peel stress sigma(yy) and the transverse shear stress sigma(xy) became dominant along the free edges of the adhesive layer. In addition, the von Mises stress decreased uniformly through the adherend thickness from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer. In addition, the layer number had only a minor effect on the through-the-thickness stress profiles after a layer number of 50, except for the peak stress values in the ceramic layer. In a single-lap joint fixed at two edges both adherends underwent considerable normal stress sigma(xx) concentrations varying from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer along the free edges of both adherend-adhesive interfaces, whereas the peel stress sigma(yy) and transverse shear stress reached peak levels along the left and right free edges of the adhesive layer. The layer number and the compositional gradient exponent had only minor effects on the through-the-thickness von Mises stress profiles but considerably affected the peak stress levels. The free edges of adhesive-adherend interfaces and the corresponding adherend regions are the most critical regions, and the adherend edge conditions play more important role in the critical adherend and adhesive stresses. Therefore, the first initiation of the joint failure can be expected along the left and right free edges of the upper and lower adherend-adhesive interfaces.