Using a planar model beyond the Born-Oppenheimer approximation, we study classically the dynamics of a hydrogen molecular ion interacting with an intense laser field. Regularized coordinates are used to remove the singularity of the electron-proton Coulomb interaction. We have calculated the probabilities of ionization and dissociation as functions of time, and obtained the photoelectron and the nuclear fragmentation kinetic energy distribution spectra as well as the harmonic generation spectra.