The autonomous vehicles need to cooperate with the nearby vehicles to ensure driving safety, however, it is challenging to plan and follow the desired trajectory considering the nearby vehicles. This article proposes a cooperative driving strategy for the connected vehicles by integrating vehicle velocity prediction, motion planning, and robust fuzzy path-following control. The system uncertainties are considered to enhance the cooperation between the autonomous vehicle and the nearby vehicle. With the driving information obtained from the connected vehicles technique, the recurrent neural network is used to predict the nearby vehicle velocity. A motion planner is developed to provide the reference trajectory considering the velocity prediction errors. Then, a robust fuzzy path-following controller is designed to track the planned trajectory. The CarSim simulations are conducted to validate the proposed cooperative driving strategy. The simulation results show that the autonomous vehicle can avoid collisions with the nearby vehicle by applying the proposed driving strategy in the overtaking and the lane-changing scenarios.