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In this study, we present a novel finite element approach to simulate crack propagation in shell structures. A local spider-web mesh is placed at the tip of a crack propagating through a global background mesh. Interface shell elements with assumed natural strains are used to connect a non-matching interface between the background mesh and the local spider-web mesh. Interface shell elements are also employed for trimmed shell elements created by cutting shell elements with the crack line. Numerical simulation of crack propagation in shell structures can be easily performed by moving the local spider-web mesh with an incremental crack growth. Numerical experiments show that the present method is very efficient and effective to accurately simulate crack propagation in shell structures without significantly increasing computational burden and implementation complexity of remeshing process.