Using the first-principles method based on density-functional theory and nonequilibrium Green's function, electronic properties of zigzag phosphorene nanoribbons (ZPNRs) terminated with nonmetallic (NM) atoms such as H, C, F, N, O, S and Si, as well as a pristine case, are studied systematically. Three possible cases are considered, namely, ZPNRs with symmetrical edge terminations, asymmetrical edge terminations, and the half-bare edge case. It is shown that the pristine ZPNRs show metallic behavior. For ZPNRs terminated with C, O, S and Si atoms, they are always metals regardless of the termination cases. For ZPNR terminated with H, F, and N, the electronic structure is either a metal or a semiconductor, which depends on the termination cases. The results from the calculated edge formation energy show that the ribbons with C, F, N, O, S and Si atom edge modifications are more stable than the H-terminated ZPNR. Moreover, an applied external transverse electric field can effectively modulate the bandgaps of ZPNRs terminated with H, F and N, especially reducing the gap with the increase of the applied external transverse electric field strength.The ZPNRs terminated with N undergo a semiconductor-to-metal transition. We also investigate the electronic transport properties in nano devices consisting of the ZPNRs terminated respectively by O and S at both edges and with the fully bare edge. It is found that O and S terminated ZPNR devices have a good linear response on bias, and the current is bigger than the pristine case. The results indicate that the introduction of NM atoms at the edge(s) can effectively modulate the electronic and transport properties of ZPNRs. These novel electronic properties suggest that PNRs are a promising candidate for future nanoelectronic and optoelectronic applications.