The existence of faulty sensor measurements in wireless sensor networks (WSNs) will cause not only a degradation of the network quality of service but also a huge burden of the limited energy. This paper investigates using the spatial correlation of sensor measurements to detect the faults in WSNs. Specially, (1) a novel approach of weighting the neighbors' measurements is presented, (2) a method to characterize the difference between sensor measurements is introduced, (3) a weighted median fault detection scheme (WMFDS) is proposed and evaluated for both binary decisions and real number measurements. Theoretical analysis and simulation results show that the proposed WMFDS can attractively obtain the high detection accuracy and considerably reduce the false alarm probability even in the existence of large fault sets. It is demonstrated that the proposed WMFDS is of excellent performance in fault detection for WSNs.