To reduce the fuel consumption and emissions of drivers passing through signalized intersections, this research proposes a fuel-saving and emissions-reducing strategy at a signalized intersection which takes into account driver's bounded rationality and speed guidance, including the theoretical basis of strategy, the scenario division of vehicle speed guidance, and the solution of vehicle optimal trajectory. Drivers are divided into three types: aggressive, normal, and conservative. Bounded rationality is divided into three levels: low, medium, and high. And the 3 x 3 x 3 numerical simulation experiments are carried out under low, medium, and high traffic flow. The results show that when the speed guidance is received, aggressive drivers have the greatest fuel-saving and emissions-reducing benefits, followed by conservative drivers. When the bounded rationality level changes under high traffic flow or the level of traffic flow and bounded rationality change concurrently, the benefits will be greatly affected. The driver's bounded rationality harms fuel consumption and emissions, and this negative effect increases with the increase of traffic flow. Providing corrected speed guidance can effectively reduce the negative effect. This study can provide more effective guidance information for drivers in a manual driving environment.