The electronic structures and magnetic properties of stanene nanoribbons (SnNRs) were studied using first-principle calculations, considering the spin–orbit coupling (SOC) effects and edge passivation. The results show that all considered armchair SnNRs are nonmagnetic semiconductors with gap values as a periodic oscillation function of ribbon width. The zigzag SnNRs present the antiferromagnetic ground states with opposite spin order between the two edges, and the gaps decrease as the ribbon widths increase. The influences of dangling bonds are obvious on the ferromagnetic moments of zigzag SnNRs. The SOC effects can open the band gap values of stanene sheets and zigzag SnNRs, but reduce the band gap of armchair SnNRs, which indicates that stanene nanostructures may be applied in the fields of spinelectronics and quantum spin Hall.