The magnetic properties of as-grown single-crystal SrMn3O6−δ nanoribbons synthesized by a simple molten-salt method can be significantly improved by a heat-treatment procedure, which enhances the ferromagnetism and spin-glass behavior. These enhanced properties might originate from a spin structure modulated by the thermodynamical equilibrium nonuniform oxygen distribution. Measurements of ac susceptibility prove the existence of a spin-glass phase in the postgrowth annealing SrMn3O6−δ nanoribbons, which differs from the only antiferromagnetic phase in the corresponding bulk material. Asymmetric magnetization hysteresis loops observed in applied magnetic fields H≤5 T are attributed to an exchange coupling between the spin-glass shell and the antiferromagnetic core of postgrowth annealing SrMn3O6−δ nanoribbons. Results suggest that the intrinsic phase inhomogeneity due to the surface effects of the nanostructural manganites may induce exchange anisotropy, which is of special interests for potential application in multifunctional spintronic devices.