Abstract: A new algorithm of the extended finite element method based on CB shell element is established in this paper to simulate arbitrary crack growth on shells. The construction of the enriched shape functions and the calculation of the stress intensity factors are both complemented in the body element, which is suitable for the condition of complicated three-dimensional fracture problems. Due to the advantage of CB shell, the variation of the shell thickness is concerned during the computation. Numerical results show that the propagation path of a crack on the shell can be independent of the mesh and the stress field can be accurately captured at the crack tip because of the enriched shape functions with singularity properties.