Abstract: The scheme for the cross-section damage defects in a circularly curved beam is established to simulate the depth, the location and the number of multiple cracks, through implementing cross-section reduction induced by microcrack damage. The h-version adaptive finite element method of a variable cross-section Timoshenko beam is introduced to solve the free vibration of a circularly curved beam with cracks damage. Using the proposed method, the final optimized meshes and high-precision solution of natural frequency and mode shape satisfying the preset error tolerance can be obtained, and the disturbance behavior of multi crack damage on the vibration mode of a circularly curved beam is studied. Numerical examples show that the non-uniform mesh refinement can adapt to the change of mode of vibration induced by crack damage, which is applied to the free vibration research of various circularly curved beams with included angles and crack damage distribution conditions. Furthermore, the influences of crack damage depth, crack damage number, and crack damage distribution on the natural frequency and mode of vibration of a circularly curved beam are quantitatively analyzed, and the accuracy and practicability of the proposed algorithm are verified.