Based on first-principles calculations, we present a systematic investigation on the electronic and magnetic properties of armchair phosphorene nanoribbons (APNRs) functionalized by 3d transition metal (TM) atoms. We found that central hollow site is the most favorable adsorption site for Mn, Co and Ni, while Fe prefers to occupy the edge hollow site. All the TM atoms bind to the adjacent P and their adsorption energies are in the range of -4.29 eV to -1.59 eV. Meanwhile, the large ratio of the adsorption energy to the cohesive energy of the metal bulk phase indicates that TM atoms prefer the 2D growth mode on the edge hydrogenated armchair phosphorene nanoribbons (H-APNRs). The magnetic moments reduce about 2-4 uB referred to their free atom states, depending on whether the TM atom is in the high-spin or low-spin state. The reduction is mainly attributed to the electrons transferring from high-level TM 4s to the low-lying 3d shell. Our results demonstrate that TM atoms adsorption is a feasible approach to functionalize the H-APNRs chemically, which results in peculiar electronic and magnetic properties for potential applications in nano-electronics and spintronics.