Results of theoretical and experimental magneto-optical studies of free excitons in wurtzite GaN are presented. The direct photoluminescence from free exciton states of high-quality GaN epilayers was studied by polarization-dependent magneto-optical measurements in magnetic fields up to 15 T. Zeeman splittings and diamagnetic shifts of the n = 1 and n = 2 states of the A exciton were observed for magnetic fields parallel and perpendicular to the hexagonal axis. The experimental data are described by a theory of the exciton energy structure in hexagonal semiconductors with wurtzite symmetry in the framework of the quasi-cubic approximation.