Exploring stable two-dimensional (2D) crystalline structures of phosphorus with tunable properties is of considerable importance partly due to the novel anisotropic behavior in phosphorene and potential applications in high-performance devices. Here, 21 new 2D phosphorus allotropes with porous structure are reported based on topological modeling method and first principles calculations. We establish that stable 2D phosphorus crystals can be obtained by topologically assembling selected phosphorus monomer, dimer, trimer, tetramer, and hexamer. Nine of reported structures are predicted to be more stable than white phosphorus. Their dynamic and thermal stabilities are confirmed by the calculated vibration spectra and Born-Oppenheimer molecular dynamic simulation at temperatures up to 1500 K. These phosphorus porous polymorphs have isotropic mechanic properties that are significantly softer than phosphorene. The electronic band structures calculated with the HSE06 method indicate that new structures are semiconductors with band gaps ranging widely from 0.15 to 3.42 eV, which are tuned by the basic units assembled in the network. Of particular importance is that the position of both conduction and valence band edges of some allotropes matches well with the chemical reaction potential of H-2/H+ and O-2/H2O, which can be used as element photocatalysts for visible-light-driven water splitting.