Using first-principles calculations based on density functional theory and projector augmented wave method, we investigate the geometric structures, magnetic properties and electronic structures of h-BN monolayer with nitrogen vacancy (VN), nitrogen substituted by oxygen (ON) or sulfur (SN). The results show that the h-BN monolayer with SN presents a larger geometric distortion than with ON and VN. Although the pure h-BN is non-magnetic, all the systems with defects are magnetic with the magnetization value of 1 μB per cell. Spin polarized density of states and energy band structures are presented. By using symmetrical analyses and molecular orbit theory, the formations of impurity energy levels and local magnetic moment are well explained.