Long queues of vehicles are often found at signalized intersections, which increases the energy consumption of all the vehicles involved. This paper proposes an enhanced eco-approach control (EEAC) strategy with consideration of the queue ahead for connected electric vehicles (EVs) at a signalized intersection. The discharge movement of the vehicle queue is predicted by an improved queue discharge prediction method (IQDP), which takes both vehicle and driver dynamics into account. Based on the prediction of the queue, the EEAC strategy is designed with a hierarchical framework: the upper-stage uses dynamic programming to find the general trend of the energy-efficient speed profile, which is followed by the lower-stage model predictive controller to computes the explicit solution for a short horizon with guaranteed safe inter-vehicular distance. Finally, numerical simulations are conducted to demonstrate the energy efficiency improvement of the EEAC strategy. Besides, the effects of the queue prediction accuracy on the performance of the EEAC strategy are also investigated.