In this study, the frictional contact problem of a functionally graded (FG) monoclinic layer was addressed based on the linear elasticity theory. The FG monoclinic layer was loaded by a rigid cylindrical punch that transmits both normal and tangential concentrated loads. It was assumed that the elastic stiffness coefficients varied exponentially through the thickness of the layer. The contact area was assumed to be under Coulomb friction conditions that relate the tangential traction to the normal component. The general expressions of the stress and displacement for the FG monoclinic layer were obtained by applying the integral transform technique. Using the boundary conditions of the problem, a second kind singular integral equation was obtained, and it was solved numerically by applying the Gauss-Jacobi integration formulas. The effect of the fiber angle, the material inhomogeneity, the friction coefficient, the punch radius, material type and the external load on the contact width, contact stress, and in-plane stress were given. This is the first study that investigates the effect of inhomogeneity on the contact problem of monoclinic materials.