We report a first-principles theoretical approach for analyzing linear and circular photogalvanic effects (PGEs) based on density functional theory within the nonequilibrium Green's function formalism. Using this approach we investigate the PGE phenomena in monolayer black phosphorus (MBP) doped with sulfur atoms. The impurity doping breaks the space inversion symmetry of pristine MBP, leading to a C s symmetry with a mirror reflection plane normal to the zigzag direction of the MBP lattice. Governed by this symmetry, a linear PGE is induced in both zigzag and armchair directions, and a circular PGE is induced along the zigzag direction. A robust broadband photoresponse is found from the near-infrared to the visible range for the MBP device. There is a strong anisotropy in PGE: photoresponse in the zigzag direction can be larger by an order of magnitude than that in the armchair direction. We identify the origin of the observed PGE as the inter-band transitions from the impurity and valence bands to the conduction bands, which involves a transfer of angular momentum from photons to electrons.