The development of connected vehicle (CV) technology has created conditions for improving the traffic efficiency of intersections and provided support for more effective speed guidance at signalized intersections. First, this paper proposes a platoon speed guidance strategy to reduce the fuel consumption and delay of the platoon passing through the intersection and smooth traffic oscillation, which includes constant speed guidance, deceleration guidance, acceleration guidance, and stop guidance. Then, the optimal speed calculation method is designed, including the calculation of the platoon’s passable period and maximum number of passing vehicles, the platoon restructure method, the analysis of the trajectory of the vehicles, and the calculation of the optimal trajectory of the platoon based on the goal of minimum fuel consumption and delay. Finally, eight different intersection scenarios are designed to simulate the proposed platoon speed guidance strategy. The results show that the platoon speed guidance strategy can effectively reduce the fuel consumption and delay of the platoon passing through the intersection and smooth traffic oscillation. In addition, the influences of queue length and CV penetration rate on the platoon speed guidance strategy are also discussed. The results show that when the queue length affects the passable period, the improvement in fuel consumption, drive time, and delay will decrease as the queue length increases. And as the penetration rate increases, the strategy becomes increasingly effective in reducing the delay and fuel consumption of the platoon in general.