Compared to fossil fuel-based internal combustion vehicles, electric vehicles with lower local pollution and noise are becoming more and more popular in urban logistic distribution. When electric vehicles are involved, high-quality delivery depends on energy consumption. This research proposes an electric vehicle routing problem considering time windows under energy consumption uncertainty. A mixed-integer programming model is established. The robust optimization method is adopted to deal with the uncertainty. Based on the modification of adaptive large neighborhood search algorithm, a metaheuristic procedure, called novel hybrid adaptive large neighborhood search, is designed to solve the problem, and some new operators are proposed. The numerical experiments show that the proposed metaheuristic can obtain high-performance solutions with high efficiency for large-scale instances. Furthermore, the robust solution based on the proposed model can achieve a satisfactory tradeoff between performance and risk.