Abstract: A parallel software module of FMM (fast multipole method) for three-dimensional Laplace kernel functions, JASMIN-3DLapFMM, is designed and implemented. The module is based on two phases parallel strategy of both processes and threads. A parallel software module is successfully used to solve the far field potential of electrostatic fields. With a fixed problem size of single processor,almost linear weak parallel scalability is obtained for a grand scale problem with 10¹⁰ particles on more than ten thousand processors. With a fixed size of total problem and 1024 processors, about three times speedup is obtained on four threads.