Bilayer graphene nanoribbon with zigzag edge is investigated with the tight binding model. Two stacking structures, a and b, are considered. The band splitting is seen in the a structure, while the splitting in the wave number direction is found in the b structure. The local density of states in the b structure tend to avoid sites where interlayer hopping interactions are present. The calculation is extended to the boron carbon nitride systems. The qualitative properties persist when zigzag edge atoms are replaced with borons and nitrogens.