The realization of strong magnetoelectric (ME) coupling for efficiently controlling of magnetism is urgently needed but still a significant challenge. Based on first-principle calculations and effective Hubbard models, we demonstrated that the polar charges and locality of edge states in hexagonal BN nanoribbons (BNNRs) play key roles in the behavior of edge magnetism M. By applying a transverse electric field, the magnetism in both zigzag and armchair edges can be regulated sufficiently. In particular, the magnetic on/off switches can be realized in armchair edges, it is robust against various edge decorations including hydrogenation, fluoridation and hydroxylation. Furthermore, uniaxial tensile strains can also produce significant magnetic modulation in Z-BNNRs, which stem from the piezoelectricity. All these suggest that h-BNNRs are ideal platforms for ME coupling researching and promising candidates for functional spintronics application.