Abstract: It extends the p-type superconvergence recovery method to the finite element analysis of the out-of-plane free vibrations of planar curved beams. Based on the superconvergence properties on frequencies and nodal displacements in modes, a linear ordinary differential boundary value problem (BVP) which approximately governs the mode on each element is set up. This linear BVP is solved by using a higher order element from which the mode on each element is recovered. By substituting the recovered mode into the Rayleigh quotient, the frequency is recovered. This method is a post-processing approach. Its recovery computation for each element is handled only on its own domain. It can enhance the accuracy and convergence rate of the frequencies and modes significantly with a small computation cost. Numerical examples demonstrate that the method is stable, efficient and worth further exploring.