The HCO+ ion plays an important role in the chemistry of interstellar space and in combustion flames. The 1 (1) Pi state is the only dissociative state below the hydrogen ionization potential, to which transitions are dipole allowed. Ab initio MRD-CI calculations have been performed for the two-dimensional potential energy surfaces of the ground state and the 1 (1) Pi state of HCO+ as functions of the C-H and C-O bond distances, keeping the ion in the Linear configuration. The 1 (1) Pi state is interesting because of an avoided crossing with the 2 (1) Pi state. The potential energy surfaces and geometry dependent dipole transition moments have been employed in two-dimensional photodissociation dynamics calculations. Total and vibrationally resolved partial cross sections are calculated as functions of the excitation energy. The potential barrier arising from the avoided crossing leads to vibrational resonances in the cross sections, which correspond to levels of the upsilon(3) (C-O) stretching motion in the excited state. The structure of the cross sections reveals the competition between resonant and direct photodissociation. The difference between the total cross section derived from the Fourier transform of the autocorrelation function and from the sum of the partial cross sections of the CO++H dissociation channel indicates the existence of a second photodissociation channel leading to CH++O. The total and partial cross sections of this channel have been computed in an independent calculation; its contribution to the integrated total cross section amounts to about 4%.