Abstract: Based on the inverse method, analytical solutions are obtained for a functionally graded curved-beam which is subjected to a moment force at the free end. Elastic properties within a curved-beam is assumed to vary in the radial direction, according to a power law, i.e. E = E₀rⁿ. In virtue of the elastic theory of plane problems, the bending solution of functionally graded curved-beam is derived. Then, the analytical solutions of a circular ring and edge dislocation are presented. Degenerated results for homogeneous elastic case are coincided well with the existing analytical solutions. Finally, numerical case studies are performed, and the results show that the stress and displacement fields are greatly influenced by graded factor n. The analytical solutions can be used as benchmark results to optimally design the functionally graded curved-beams.