<p>Based on the nonlocal strain gradient theory and high-order surface stress model, the mechanical properties on bending and vibration of functionally graded graphene-reinforced composite curved nanobeam are investigated. The general governing equations for the dynamic behavior of curved nanobeam are formulated. The Halpin–Tsai model and the mixture rule are utilized to estimate the effective Young’s modulus and Poisson’s ratio of composite curved beams. The influences of graphene mass fraction, graphene sheet distribution type, beam radian, and high-order surface effect on the mechanical properties of bending and vibration of curved beam are analyzed. In addition, the dependences of the beam deflection, axial displacement and rotation degree in the process of beam vibration on the width-to-thickness ratio and aspect ratio of graphene sheet are discussed. The rationality and applicability of the present model are validated. It is demonstrated that the graphene sheets, the beam radian, and the high-order surface effects on the bending and vibrational properties of curved beam are significant.</p>