A new Distributed Fault Detection Algorithm(DFDA) is proposed to solve the node fault problem in wireless sensor networks. The DFDA algorithm uses the node degree information to estimate the importance of the node to the network, and saves the node with high node degree to the network as much as possible. The fault nodes are detected by comparing the sensing data among nodes. In order to enhance the accuracy of the detection, a double determination strategy is adopted. The simulation results show that the DFDA algorithm improves the accuracy of detecting fault nodes and reduces the false alarm rate compared with similar algorithms.