Previous studies have proposed various algorithms such as model predictive control, machine learning, and dynamic programming for ecological adaptive cruise control (ACC). However, industrial application of these algorithms is limited owing to their considerable computational cost. Moreover, there is a tradeoff between the calculation time and optimization results. In this study, a novel optimization method, referred to as quadrant dynamic programming (QDP), for ACC is proposed. QDP is based on regular dynamic programming (DP); it divides the DP table into four quadrants. Most of the computations are performed offline, and expensive hardware is not required to be installed in vehicles. Moreover, the offline computation cost is also reduced to a practical level, whereas the result is globally optimal. The algorithm is validated for reducing the energy consumption of an electric vehicle (EV) via simulations and experiments using our test vehicle. The experimental results also showed the accuracy of the motor and vehicle dynamics models. Compared with the widely used ACC for feedback control, QDP reduced energy consumption by 16.1 % in multi-lane car following scenarios with the same cruising distance and time. The proposed QDP avoided trade-offs between computational cost and optimization results by utilizing offline computation effectively. Moreover, it was proven valid for general ecological ACC applications.