In order to simulate the distribution of magnetic field generated by cardiac electrophysiological activities, a three-dimensional (3D) computing framework of magnetocardiogram forward problem based on a finite element method (FEM) is proposed. First, the 3D heart-torso geometry model is established from the 3D reconstruction of magnetic resonance images. Then the modified FitzHugh-Nagumo (FHN) equation combined with 3D cardiac geometry is used to investigate the propagation of transmembrane potential (TMP). In the end, quasi-static Maxwell equations and 3D torso model are used to explore the propagation of the bioelectromagnetic field produced by TMP. In our calculation, the Galerkin finite element method is used. The results show that the FEM-model can simulate extracorporeal magnetic field. Further, numerical solutions of simplified models with the one-dimensional FHN equation and the straight wire are respectively consistent with the analytical solutions, which verifies the feasibility of the computing framework. In summary, this framework successfully simulates the cardiac TMP and extracorporeal magnetic field, which may conduce to the study of magnetocardiogram inverse problem.