A multiscale approach based on the mesh superposition method is applied to unidirectional CFRP laminates to evaluate the influence of the singular deformation field at the free-edge region on crack formation. In our multiscale approach, two different scale analyses are employed. First one is a local analysis utilizing a model composed of carbon fibers with micron-scale diameters and matrix resin. Two failure criteria are applied to the matrix resin to predict the matrix cracks which occur under elastic deformation and plastic deformation. Second one is a global analysis which employs a homogenized model assumed to be an anisotropic elasto-plastic body. The global analysis is conducted to evaluate the macroscopic deformation behavior of laminates. The local model is superimposed on the global model, maintaining the continuity of the displacement field between global and local domains. The local analysis is then performed to predict crack initiation and crack propagation, using the displacement field obtained from the global analysis. The global analysis and the local analysis are conducted iteratively to obtain the convergence results considering the interaction between macroscopic deformation behavior and heterogeneity of the material. The multiscale approach is applied to the tensile tests of the unidirectional CFRP laminates under off-axis loading to predict the failure strain. Our simulated results reveal that the initial crack occurring on the free-edge region doesn't affect the failure strain.