China's energy demand is growing rapidly and large hydropower plants are becoming more common. This therefore has resulted in the building of many large concrete dams across the country. Significant dam cracking can have major environmental, economic and social consequences. Collapse of High concrete dam may cause serious harm to economic development as well as safety of the people; thereby necessitating the need for research on safety and stability of high concrete dam under high water and seismic conditions. In this paper, the high concrete dam of Longtan was used as an example, using the ABAQUS program based on the extended finite element method to analyze the Longtan Dam under static and dynamic conditions which has been commonly used for the study of crack growth. A numerical prediction of crack propagation in concrete gravity dams is presented. The two-dimensional seismic numerical study was done using acceleration-time records from Koyna earthquake in 1976 Dam concrete cracking range and cracking were discussed during a seismic time. The locations that are easy to generate cracks are illustrated from the analysis and the findings showed that, during seismic activity the Longtan Dam was rather unsafe. The results of the work can provide a valuable guide for the design and operation of the dam system.