In this paper, a bus priority signal control (BPSC) method based on delays of passengers and pedestrians at adjacent intersections, is proposed. The influences of BPSC on passenger and pedestrian delay at adjacent intersections under the condition of coordinated control of green waves are studied. The implementation of BPSC at intersections not only reduces the delay of bus passengers, social vehicle passengers and pedestrians, but also improves the traffic flow of priority buses and social vehicles at downstream intersections. This study takes the green phase extension as an example of the active BPSC strategy, and analyzes three cases of priority vehicles reaching downstream intersection. Firstly, passenger and pedestrian delays at adjacent intersections are calculated under different traffic situations. Secondly, models with the goal of maximizing the reduced total delays are established. Thirdly, three algorithms are used to solve the problem to obtain the optimal signal timing adjustment scheme at upstream intersections. Ultimately, the result shows that the BPSC can effectively reduce pedestrian delays at intersections, protect the rights and interests of pedestrians, reduce the delays of priority vehicles, and maximize the reduced total delay.