•Propose a multi-stage optimal control problem to minimize vehicle fuel consumption.•Consider the impacts from queue on the optimal vehicle speed trajectory.•Develop a constrained optimization model to solve the problem efficiently. Vehicle speed trajectory significantly impacts fuel consumption and greenhouse gas emissions, especially for trips on signalized arterials. Although a large amount of research has been conducted aiming at providing optimal speed advisory to drivers, impacts from queues at intersections are not considered. Ignoring the constraints induced by queues could result in suboptimal or infeasible solutions. In this study, a multi-stage optimal control formulation is proposed to obtain the optimal vehicle trajectory on signalized arterials, where both vehicle queue and traffic light status are considered. To facilitate the real-time update of the optimal speed trajectory, a constrained optimization model is proposed as an approximation approach, which can be solved much quicker. Numerical examples demonstrate the effectiveness of the proposed optimal control model and the solution efficiency of the proposed approach.