Vehicle re-identification is a challenging task that matches vehicle images captured by different cameras. Recent vehicle re-identification approaches exploit complex deep networks to learn viewpoint robust features for obtaining accurate re-identification results, which causes large computations in their testing phases to restrict the vehicle re-identification speed. In this paper, we propose a viewpoint robust knowledge distillation (VRKD) method for accelerating vehicle re-identification. The VRKD method consists of a complex teacher network and a simple student network. Specifically, the teacher network uses quadruple directional deep networks to learn viewpoint robust features. The student network only contains a shallow backbone sub-network and a global average pooling layer. The student network distills viewpoint robust knowledge from the teacher network via minimizing the Kullback-Leibler divergence between the posterior probability distributions resulted from the student and teacher networks. As a result, the vehicle re-identification speed is significantly accelerated since only the student network of small testing computations is demanded. Experiments on VeRi776 and VehicleID datasets show that the proposed VRKD method outperforms many state-of-the-art vehicle re-identification approaches with better accurate and speed performance.