Gradual variation of the elastic properties in FGMs enables elimination or reduction of the elastic mismatch at the interface between the coating and the substrate. As a consequence, the reduction in the residual stress level, improvement of the bonding strength, and the crack stabilization are achieved at the interface. This study focuses on the mathematical modeling of the rolling contact problem of an FGM coating-substrate system. The fully coupled rolling contact problem of a graded coating is provided for all possible stick/slip scenarios. The governing equations of the relevant rolling contact problem are constructed by means of the singular integral equations approach. Later, the Gauss-Chebyshev numerical integration method is utilized to discretize the governing equations into systems of algebraic equations. Finally, some numerical algorithms are proposed to solve these systems of algebraic equations. Comprehensive parametric study is performed to examine the effects of material properties, coefficient of friction, coating thickness and external loads on the surface stress components, the stick/slip configurations, the creep ratio and the power loss.