BeiDou navigation satellite system (BDS) is one of the four main types of global navigation satellite systems. The current system has been widely used by the military and by the aerospace, transportation, and marine fields, among others. However, challenges still remain in the BeiDou system, which requires rapid responses for delay-sensitive devices. A differential positioning algorithm called the data center-based differential positioning (DCDP) method is widely used to avoid the influence of errors. In this method, the positioning information of multiple base stations is uploaded to the data center, and the positioning errors are calculated uniformly by the data center based on the minimum variance or a weighted average algorithm. However, the DCDP method has high delay and overload risk. To solve these problems, this paper introduces edge computing to relieve pressure on the data center. Instead of transmitting the positioning information to the data center, a novel method called edge computing-based differential positioning (ECDP) chooses the nearest reference station to perform edge computing and transmits the difference value to the mobile receiver directly. Simulation results and experiments demonstrate that the performance of the ECDP outperforms that of the DCDP method. The delay of the ECDP method is about 500ms less than that of the DCDP method. Moreover, in the range of allowable burst error, the median of the positioning accuracy of the ECDP method is 0.7923m while that of the DCDP method is 0.8028m.