Multi-sensor multi-target tracking (MMT) is widely used in civilian and military fields. However, as the number of sensor nodes increases, so does the probability of the sensor node faults corrupting the system. In order to guarantee the tracking performance in the presence of faulty sensors, a distributed MMT algorithm in clutter with sensor fault detection and exclusion under the belief propagation framework (FDE-BP) is proposed in this paper. Firstly, a novel FDE method using the fused residual is proposed to detect the faulty sensors in clutter. To ensure the independence among the fused residuals of different targets, a measurement partition method based on the assignment matrix is proposed. The partition of measurements makes the factor graph have a tree structure rather than a loop one, which reduces the computational complexity. Secondly, the MMT problem is presented by a factor graph model to fuse the information among distributed sensor nodes, and a Gaussian version of FDE-BP is derived. The simulation results show that the proposed FDE-BP algorithm can guarantee the tracking performance in the presence of different types of sensor faults.