Max-pressure signal control has been analytically proven to maximize the network throughput and stabilize queue lengths whenever possible. Since there are many transit lines operating in the metropolis, the max-pressure signal control should be extended to multi-modal transportation systems to achieve more widespread usage. The standard max-pressure controller is more likely to actuate phases during high-demand approaches, which may end up ignoring the arrival of buses, especially in bus rapid transit. In this paper, we propose a novel max-pressure signal control that considers transit signal priority of bus rapid transit systems to achieve both maximum stability for private vehicles and reliable transit service. This study revises the original max-pressure control to include constraints that provide priority for buses. Furthermore, this policy is decentralized which means it only relies on it relies only on the local conditions of each intersection. We set the simulation on the real-world road network with bus rapid transit systems. Numerical results show that the max-pressure signal control which considers transit signal priority can still achieve maximum stability compared with other signal control integrated with transit signal priority. Furthermore, the max-pressure control reduces private vehicle travel time and bus travel time compared to the current signal control.