The finite-difference time-domain (FDTD) method is useful in solving three-dimensional (3D) electromagnetic problems. However, it contains a numerical instability because it is a complete explicit method, and huge amounts of memory are required in the case of 3D analysis. The implicit FDTD method called the Alternating Implicit Block Overlapped (AIBO)-FDTD method was proposed for two-dimensional (2D) electromagnetic analysis. In our study, the 3D AIBO-FDTD method is developed by the modification of the 2D method. This method is suitable for parallel processing since the computational domain can be effectively partitioned. This property is especially compatible with implementations using distributed-memory multiprocessor systems such as PC clusters, which provide a huge memory space that accommodates a large problem. Although this method seems numerically stable since the implicit scheme is included, our result shows that the numerical instability occurs when the time step exceeds Courant's stability condition. This condition is still more relaxed than the conventional FDTD method. Furthermore, we demonstrated that parallel processing is an effective technique for improving the performance of the 3D AIBO-FDTD method, while this method is slower than FDTD when it is run on one processor.