We report on the optical saturable absorption of few-layer black phosphorus nanoflakes and demonstrate its application for the generation of vector solitons in an erbium-doped fiber laser. By incorporating the black phosphorus nanoflakes-based saturable absorber (SA) into an all-fiber erbium-doped fiber laser cavity, we are able to obtain passive mode-locking operation with soliton pulses down to ~670 fs. The properties and dynamics of the as-generated vector solitons are experimentally investigated. Our results show that BP nanoflakes could be developed as an effective SA for ultrashort pulse fiber lasers, particularly for the generation of vector soliton pulses in fiber lasers.