Analytical solution of eddy current problem for a moving medium is obtained in the present paper. A single-turn circular coil is located above a conducting two-layer medium. The upper layer is moving in a horizontal direction with constant velocity. The lower layer of the medium is fixed. The electrical conductivity and magnetic permeability of the upper layer are exponential functions of the vertical coordinate. The solution is found by the method of Fourier integral transform. The change in impedance of the coil is obtained in terms of double integral containing Bessel functions. A particular case of a moving half-space with varying properties is considered in detail. The solution can be generalized for the case of a moving multilayer medium.