According to density functional first-principles calculations, we study the electronic and magnetic properties of two-dimensional h-BN containing lattice vacancies: B atom vacancy (VB), N atom vacancy (VN) and BN pair vacancies (VBN). In microstructures, the neighbored N atoms around vacancy in VB system are constructed into an isosceles triangle; the neighbored B atoms around vacancy in VN system are constructed into an equilateral triangle; and the neighbored atoms around BN pair vacancies are constructed into a keystone. The calculations on band structures and density of states show that the significant spin polarization exists in two-dimensional h-BN containing single vacancy defects, while the BN pair vacancy system exhibits non-spin polarization. Three kinds of vacancy defects make the band gap change from direct band gap to indirect band gap. For the VB system, the total magnetic moment is 1.00 μB, due to the contribution from the neighbored N atoms around vacancy. The directions of magnetic moment in three neighbored N atoms around vacancy are different. Among them, ferromagnetic and anti-ferromagnetic coupling are coexisting. For the VN system, the total magnetic moment in the entire calculated supercell is also 1.00 μB and presents a certain distribution in the area around the vacancy.