The development of computer hardware technology has made numerical calculations of large-scale complex mechanical problems more efficient. To reduce the computational time in the fields of coupled finiteelement and discreteelement (FEM-DEM), an efficient asynchronous step integration parallel computational algorithm based on overlapping boundary was proposed. The whole model was divided into an FEM subdomain and a DEM subdomain, where the integral step size was depended on the element characteristics of the subdomain. An explicit time integral scheme was adopted in both subdomains. The method of overlapping boundary was adopted to handle the interface coupling problem, introducing the continuity transfer of overlapping boundary data into parallel computing, utilizing dynamic overlapping boundary methods and interprocess communication to transfer boundary information between adjacent subdomains, without the interpolation process in the subcycling process. The use of overlapping bonndaries can effectively reduce computational erros, and compared to the transition errors and the transition layer algorithm, the overlapping boundary area was small and easy to operate. Numerical examples showed that the algorithm proposed can improve the computational efficiency with a high computational accuracy. The research result can provide ideas for the calculation of largescale coupled finite element discrete element problems.