There have been studies for the crack propagation simulation such as the node release technique, the element elimination method, the cohesive zone model, the extended finite element method, etc. Among these methods, the cohesive zone model is known as an effective method for the crack initiation and propagation. The cohesive zone model is easy to implement in a finite element code and estimates accurately the experimental results. Unfortunately, it has some drawbacks. The crack path is already known for the crack propagation because the cohesive elements are already generated on the crack path. Additionally, it is difficult to generate the cohesive element because the thickness of the cohesive element is very thin. In this study, an effective method by using the superimposed finite element method is proposed to overcome these drawbacks. The superimposed finite element method is one of the local mesh refinement methods. A fine mesh is generated by overlaying the patch of the local mesh on the existing mesh called the global mesh. Thus, re-meshing is not required. When the crack propagates, the local mesh refinement by using the superimposed finite element method is operated using the local element patch. The mesh of the local element patch includes the crack and the cohesive elements are generated on the crack surface of the local element patch. Therefore, the crack propagation simulation can be performed along the new crack path. Also, some local mesh patches are classified as the direction of the crack propagation in the proposed method and the local mesh patch is generated using the hierarchical concept. Then, the generation of the local mesh patch is easy and efficient. Additionally, the re-meshing process is not required. Consequently, the proposed method improves the efficiency of the crack propagation simulation. The proposed method is applied to several examples.