Axisymmetric contact problem on indentation of a rigid circular or spherical punch into an elastic transversely-isotropic half-space with a transversely-isotropic piezoelectric functionally graded coating is considered.Elastic moduli,piezoelectric constants and dielectric permeabilities of the coating vary with depth according to arbitrary functions.Problem is reduced to the solution of a dual integral equation.Using the approximation of the kernel transform by the product of fractional quadratic functions the approximated solution of the dual integral equation is constructed in analytical form.Some asymptotic properties specify difference between the half-space with or without a coating are obtained analytically.Numerical results illustrating the elastic deformation of transversely-isotropic half-space with a coating are provided for different types of variation of elastic moduli in depth of the coating in whole range of geometrical parameter of the problem.