In order to control the energy consumed by vehicles for crossing signalized intersections, this project designs and tests a speed guidance energy-saving strategy for signalized intersections, taking drivers’ bounded rationality into consideration. This research achieves speed guidance by developing theoretical foundation of speed guidance, dividing scenarios for practise of speed guidance, and calculating optimal trajectories for vehicles. As for influence of bounded rationality, this research categorizes all drivers into three different types: aggressive drivers, normal drivers and conservative drivers. Numerical simulation of this research is focuses on a single intersection, with three traffic saturation level, represented by 346, 519 and 692 vehicles per hour. Considering the foreseeable popularization of electric cars (EV) in the close future, proportion of EV is also taken as a variable, and experiments are carried separately at three milestones of EV proportion: 0%, 30%, and 60%. The findings suggest that aggressive drivers benefit the most from the speed guidance in energy saving, and speed guidance does lest benefit to normal drivers. Both drivers’ bounded rationality and high traffic volume could lead to increase of energy consumption, while providing specifically modified speed guidance is able to achieve satisfying reductions to these effects. With increase of EVs’ proportion in the traffic flow and drop of overall energy consumption, effect of the guidance becomes comparatively worse than the previous non-EV performance of 7% to 11%, while remaining to be effective to cut off overall energy consumption by 5% to 8%. This research is able to improve normal speed guidance with more accurate and practicable guidance information for drivers in current traffic environment.