To improve the accessibility of bus rapid transit (BRT) systems, the median stations are usually located beside intersections. However, due to the limited storage space at the stations, high bus volumes and fluctuant bus arrival patterns may cause queue spillbacks and consequently block the intersections. Traditional transit signal priority control could deteriorate such situations when a green extension or a red truncation is activated. Hence, it is essential to develop a new operational framework that is capable of both reducing bus travel time and preventing queue spillbacks at the median stations. This study presents a novel signal control scheme to integrate both priority (i.e. green extension and red truncation) and suppression strategies (i.e. green truncation and red extension) for approaching buses. Notably, the suppression control is only implemented to the farside directional traffic. To evaluate the proposed signal control system, this study tests the algorithms on a real BRT network in Jinan, China. Simulation results of multiple experiments show that the developed method has great promise in bus delay reduction and spillback avoidance in the station area. Other further explorations with sensitivity analysis find that the proposed control will be more effective when the signal is able to provide longer priority and suppression durations.