The ubiquity of smart-devices enables the foundation for emerging fast-growing ride-sourcing companies that challenges the traditional taxi services. A crucial aspect of designing ride-sourcing systems is matching mechanism between idle ride- sourcing vehicles and passenger travel requests (i.e. vehicle-passenger matching). Forcing ride-sourcing vehicles to pick up long-distance waiting passengers causes wild goose chase problem that can dramatically increases search time. In this paper, a non-equilibrium based spatio-temporal vehicle-passenger matching method is introduced to determine dynamically and jointly the matching time instances and maximum matching distances to minimize passengers’ waiting time (i.e. from the travel request until the pickup) while considering the level of congestion of the network. The performance of the matching method under noticeable variation of tra c congestion and passenger travel requests are investigated with microsimulation.