Recently, the ever-increasing vehicle population has become a severe challenge to traffic efficiency and air quality in modern city life. Signal-controlled intersection is a bottleneck of the urban traffic system. Platooning has the potential to improve the intersection throughput, and a typical V2X application, green light optimal speed advisory (GLOSA), can also reduce vehicles' stopping at intersections to enhance traffic efficiency. However, there is scarcely any literature regarding GLOSA system for platoon to increase intersection throughput. In this paper, the composite platoon trajectory planning strategy (CPTPS) is proposed to maximize the intersection throughput. Since the intersection throughput maximization problem can be transformed into minimizing vehicles' intersection arrival time in a green phase by optimizing vehicles' trajectories, three portions are designed in CPTPS to solve the problem, which are a GLOSA-based trajectory planning method for platoon leaders, a reinforcement learning-based trajectory planning method for platoon followers, and a flexible platoon management protocol to ensure the smooth operations in a platoon. Simulation results show that, compared to the non-optimized cases, CPTPS can effectively increase intersection throughput while reduce stoppings at intersections and gas emissions. Especially in saturation cases, CPTPS can achieve a near-ideal throughput performance. And the communication delay within 100 ms scarcely affects CPTPS's headway maintenance performance. Moreover, CPTPS outperforms the existing works in headway maintenance when vehicles drive in a platoon. These results validate the effectiveness, robustness, and practical feasibility of CPTPS, for solving the signal-controlled intersection traffic efficiency problem.