Signalized intersection has great roles in urban traffic system. The signal infrastructure and the driving behavior near the intersection are paramount factors that have significant impacts on traffic flow and energy consumption. In this paper, a speed guidance strategy is introduced into a car-following model to study the driving behavior and the fuel consumption in a single-lane road with multiple signalized intersections. The numerical results indicate that the proposed model can reduce the fuel consumption and the average stop times. The findings provide insightful guidance for the eco-driving strategies near the signalized intersections.