We report on the experimental and theoretical study of the strain splitting of nitrogen acceptor levels in epitaxially grown ZnSe on GaAs substrate. The crystal strain is due to the different lattice constants and thermal expansion coefficients and is determined by x-ray diffractometry. The binding energies of the acceptor ground and excited states have been determined by temperature-dependent and resonant photoluminescence measurements involving two-hole transitions for three differently strained levels. A consistent theoretical description of the experimental data is given in terms of the model of Baldereschi and Lipari, augmented by the Bir-Pikus Hamiltonian to account for the strain splitting of the valence-band edge. An empirical ansatz for the central-cell correction is used in order to reproduce the chemical shift of the nitrogen acceptor.