In this paper, we propose a resource allocation of device-to-device (D2D) communications underlaying multi-antenna cellular systems by employing message-passing algorithm. It is possible to construct the factor graph of the D2D pairs by considering the interference power at the base station and among the D2D pairs. The goal is to avoid interfering the cellular transmission while increasing the sum data rate of D2D pairs. We show that the proposed resource allocation based on message passing algorithm allow us to almost reach the performance of the exhaustive search and outperforms the random allocation. Since the associated factor graph is not fully connected, the complexity of the algorithm is significantly reduced compared to the exhaustive search.