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Vehicle detection is a challenging task in computer vision. In recent years, numerous vehicle detection methods have been proposed. Since the vehicles may have varying sizes in a scene, while the vehicles and the background in a scene may be with imbalanced sizes, the performance of vehicle detection is influenced. To obtain better performance on vehicle detection, a multi-scale vehicle detection method was proposed in this paper by improving YOLOv2. The main contributions of this paper include: (1) a new anchor box generation method Rk-means++ was proposed to enhance the adaptation of varying sizes of vehicles and achieve multi-scale detection; (2) Focal Loss was introduced into YOLOv2 for vehicle detection to reduce the negative influence on training resulting from imbalance between vehicles and background. The experimental results upon the Beijing Institute of Technology (BIT)-Vehicle public dataset demonstrated that the proposed method can obtain better performance on vehicle localization and recognition than that of other existing methods. [ABSTRACT FROM AUTHOR]