In this paper, the contact problem of an elastoplastic functionally graded substrate and a rigid spherical indenter is investigated using finite element method. For the first time, the proposed finite element model accounts for the smooth variation in all elastic and plastic properties through the thickness direction of the substrate according to power law and Tamura, Tomota and Ozawa (TTO) model. The proposed model is implemented into the ANSYS FE package. The results obtained from the FE analysis are verified and compared with those available in literature. An extensive parametric analysis is conducted to explore the influence of the indenter radius, gradient index, Poisson's ratio and hardening of the indented substrate on the load-indentation response, contact pressure distribution, stress and plastic strain distributions and displacement beneath the indenter. The results illustrated that the indentation responses of elastic, elastoplastic and elasto-perfectly-plastic functionally graded materials are significantly affected by the material property distribution. Finally, a simple empirical equation is presented to relate the residual indentation depth of elastoplastic functionally graded materials with the gradient index using a single material parameter. The results of this study can guide tribology engineers in determining the contact stress and indentation depth that have a great effect on the hardness and the damage of indented body.