The microscopic description of the magnetoelectric effect in LiCoPO4 is given. The "one-ion" approximation in which the magnetic order is presented by a Weiss molecular field approximation is taken as the basis of the model. Using the lowest possible order of perturbation theory the mechanism analogous to that of the changes due to an electric field of g-factor rather than a mechanism which involves changes of the quadratic axial term ("D-term") in the spin-Hamiltonian is considered. Within the framework of the model, it is shown that the odd part of the crystalline electric field and operator of the electric dipole transition can be represented by an effective operator with even parity that allows us a priori to take into account a parity selection rule. The expressions for the magnetoelectric tensor have been obtained. The theory may be applicable not only to the description of the static ME response but also to the description of the response of the system at optical frequencies.