The highway on-ramp merging area is one of the major sections that form traffic bottlenecks. In a connected vehicle environment, V2V and V2I technologies enable real-time exchange of information, including position, speed, and acceleration. To improve the efficiency of vehicle merging at the on-ramp, this study proposes a cooperative merging control strategy for network-connected autonomous vehicles. First, the central controller designs the merging sequence and safety space for vehicles passing through the confluence point. Then, a trajectory optimization model was constructed based on vehicle longitudinal dynamics, and the PMP algorithm was used to determine the optimal control input. Finally, all vehicles follow the optimal trajectory so that the ramp vehicles merge smoothly into the mainline. Simulations verify that the proposed algorithm performs better than FIFO, with 13.2% energy savings, 41.4% increase in average speed, and 50.4% reduction in travel time over the uncontrolled merging scenario. The method is further applied to different traffic flow conditions and the results show that it can significantly improve traffic safety and mobility, while effectively reducing vehicle energy consumption. However, the traffic operation improvement is not satisfactory under low traffic demand.