Autonomous driving strategies for intersection scenarios are challenging due to the varying traffic conditions of oncoming vehicles. Based on the connected vehicle technology, this article proposes an autonomous T-intersection driving strategy considering the oncoming vehicles for motion-planning and path following. A finite-state machine (FSM) is developed in the motion planner to decide the driving strategies considering the oncoming vehicles. Information pieces from the connected vehicle, specifically vehicle position and speed, are selected and effectively utilized to construct the temporal windows that manage the driving states transition of the FSM. Speed profiles in different driving states are modified for collision avoidance. Then, a path-following controller based on the back-stepping method is designed to track the planned path and speed simultaneously. The proposed strategy is validated by both simulation and experimental investigations. The results show the controlled vehicle can safely and quickly pass through the intersection using the proposed driving strategy that avoids possible collisions with the oncoming vehicles.