By using non-collinear density-functional calculations, we clarified the magnetic states of zigzag-edged graphene nanoribbons (ZGNRs). In the novel non-collinear states that were found, the angle θ between the magnetic moments at the two edges were canted, i.e., 0 <θ< 180°, which was in contrast with the case of antiferromagnetic (AFM; θ=180°) and ferromagnetic (FM; θ=0°) states. As θ increased from 0 to 180°, the band gap increased and the total energy decreased. As a result, the AFM state was the ground state and had the maximum band gap, whereas the FM state had the highest energy and no band gap. As a result of the development of nanotechnology, the magnetic fields with canted directions between the two edges can be applied. Therefore, we expect that the spin canting angle θ can be varied by the introduction of magnetic fields, so the band gap of ZGNRs can be controlled. It is thus suggested that ZGNRs are potential candidates for spintronics applications.