Through wireless communications, enriched information from connected vehicles (CVs) can describe traffic information near an intersection and would supplement a data source for an effective signal control. This paper proposes an adaptive traffic signal control system in a CV environment. At the intersection level, an adaptive control model is developed to assign optimal green times by minimizing the total vehicle delay. When the CV penetration rate is low, a method depending on limited CV data is presented to estimate the vehicle arrival information. At the corridor level, a real-time optimization model is formulated to design the dynamic progression plan for critical paths (i.e. paths with high flows). These two optimization models are solved by the dynamic programming technique. A real-world arterial is modeled in VISSIM to evaluate the effectiveness and efficiency of the proposed traffic signal control system. Simulations with various CV penetration rates and demand levels are conducted to compare the proposed system with fixed coordination and adaptive signal control systems. Results indicate that the proposed system outperforms both base systems by reducing 15.67% and 13.81% of the average delay, respectively, when the CV penetration rate is relatively high. Moreover, the proposed system can improve the arterial performance under all tested scenarios with various CV penetration rates and demand levels. Since the tested demand scenarios can reflect the real traffic fluctuations, it can be proved that the proposed control system could be applied in the field to boost the overall traffic efficiency along the arterial.