Motivated by the observation that traffic flows in urban networks may vary significantly both temporally and spatially, this paper introduces a new version of extended back-pressure (EBP) traffic signal control algorithm. This algorithm can be responsive to different traffic flows by tuning control parameters over both time and location, and it tends to minimize delay at low traffic flows by using a set of so-called stage weights. We show that under mild conditions, the EBP algorithm with time-varying control parameters can achieve maximum throughput, i.e., when the EBP algorithm is adopted, the expected long-term average of total queues is bounded from above for largest possible set of arrival vectors. A simulation based on real traffic data of Singapore demonstrates the validity of the proposed EBP algorithm.