Phosphorene has attracted great interest in spintronics. Here, the electronic structures of monolayer zigzag black phosphorene nanoribbons(ZBPNRs) are researched. We found that the magnetic ground state of ZBPNRs is dependent on nanoribbon widths. In addition, we examine the role of the surface adatoms including Li, Na, K, Mg, Ca and Al in modifying the electronic properties of ZBPNRs. Our calculations show that the adsorption systems with Li, Na and K are half-metals due to the localization of transferred charge. On the other hand, Mg, Ca and Al, which provide more valence electrons than Li, Na and K, result in a smaller net magnetic moment and prefer semiconductor or metal. Our findings propose a new approach without magnetic atoms, magnetic field and strong electric field to realize half-metal in phosphorene, which overcome the drawbacks of graphene/silicene with negligible band-gap as well as transition metal sulfide with low carrier mobility.