A new kind of hybrid graphene nanoribbon two different edges (one zigzag and another armchair) has been proposed and studied by the first principles calculations, which could be constructed by different kinds of periodical grain boundaries joining together the normal zigzag and armchair graphene nanoribbons (GNRs).It is found that the ground state of the hybrid GNR is the robust ferromagnetic (FM) with a high FM Curie temperature, which is totally different from those of the normal GNRs.Most of the hybrid GNRs are found to be FM metal, except for the type-A hybrid GNR with a very narrow width, which contains three pairs of 5-7 topological defects in a unit cell of its grain boundary.A metal-semiconductor transition can be tound in the type-A structure when its number of zigzag carbon chains decreases.More interestingly, it is found that all the hybrid GNRs, especially the type-A ones, can become half-metallic, which could be useful in the future applications of spintronics.Finally, the binding energy calculations for these hybrid GNRs show that they could be stable and possibly synthesized in future experiments.And the study of their edge defect effects indicates that their ferromagnetism and half-metallicity could survive even in existence of edge defects.