Using the first principles calculations based on the density-functional theory, we study the geometric structures, magnetisms, and electronic structures of h-BN monolayer with group IA/I!IA elements (Li, Na, K, B, Mg and Ca) replacing B as impurities. It is shown that the nonmagnetic substitutional impurities can induce spin polarization in nonmagnetic BN monolayer. For Li, Na and K impurities, the total magnetic moment of the supercell is 2 μB; for Mg and Ca, it is 1 μB. The magnetic moments are mainly localized on the nearest neighbor N atoms. The magnetic moment of the supercell with Be impurity is 0.705 μB, distributed over all N atoms. Spin polarized densities of states are presented, including total density of states and orbital-projected partial density of states. The origin of local magnetic moments and impurity energy level are explained. It is also found that the Mg and Ca doped systems are half metallic.