While connected and autonomous vehicle (CAV) technology advances intelligent transportation, the control of mixed traffic flow at signalized intersections with both CAVs and human-driven vehicles (HDVs) requires further exploration, especially concerning the backward-looking effect. This is because considering the backward-looking effect of vehicles not only aligns more closely with drivers’ habits in real-world traffic conditions but also results in a more stable platoon with smaller saturated headways compared with scenarios that only consider the vehicle ahead. By taking into account vehicles in both the front and rear directions, overall traffic efficiency is improved. Therefore, this paper proposes the “1 + n + 1” mixed platoon model, which includes one leading CAV, n following HDVs, and one trailing CAV. The leading and trailing CAVs collectively guide the intermediate HDVs at intersections, thus creating an optimal control framework for platoon-based CAVs at signalized intersections. The specific research contributions of this paper are as follows. First, a linearized dynamic model for the “1 + n + 1” mixed platoon is developed and compared with a benchmark model that controls only the lead vehicle. Next, constraints are established for the optimal control framework to improve intersection traffic efficiency and fuel economy by managing both the leading and trailing CAVs. Finally, extensive simulations compare vehicle throughput and fuel consumption under various control methods, demonstrating that incorporating both forward- and backward-looking effects significantly outperforms traditional methods focused solely on the lead CAV, with vehicle throughput increasing by up to 33% and average fuel consumption decreasing by about 21%.