We present a theoretical calculation of the fine structure of an exciton molecule bound to a nitrogen center in GaP. The conduction-band structure is properly taken into account (except for the camel's back effect) by using a combination of Wannier states and effective-mass states for the center electron. The valence-band warping is included by using s-like and d-like effective-mass states for the holes. Solving the one-exciton problem, we obtain a splitting of 0.78 meV of the J=2 and 1 levels due to the electron-hole exchange Coulomb interaction. Including the electron-hole exchange Coulomb interaction and the j-j coupling between holes in the exciton molecule gives a splitting of 0.20 meV for the lowest-lying states with total angular momenta J=0 and J=2. The results are in good agreement with experiment.