The exciton structure of crystalline MePTCDI (N-N'-dimethylperylene-3,4,9,10-dicarboximide) is modeled by a one-dimensional Hamiltonian, which includes the interactions between Frenkel excitons; with several vibronic levels and charge-transfer excitons. Using appropriate fitting parameters, which are verified by quantum chemical calculations, this model can explain the main features of the low temperature absorption spectrum. Polarized absorption spectra show different polarization ratios for the various peaks. This polarization behavior is explained by the varying contribution of the charge-transfer transition dipole, which has a direction different from the Frenkel transition dipole. Our model for the exciton band structure is supported by transient emission measurements.