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As a dynamic and essential component in the road environment of urban scenarios, vehicles are the most popular investigation targets. To monitor their behavior and extract their geometric characteristics, an accurate and instant measurement of vehicles plays a vital role in traffic and transportation fields. Point clouds acquired from the mobile laser scanning (MLS) system deliver 3D information of road scenes with unprecedented detail. They have proven to be an adequate data source in the fields of intelligent transportation and autonomous driving, especially for extracting vehicles. However, acquired 3D point clouds of vehicles from MLS systems are inevitably incomplete due to object occlusion or self-occlusion. To tackle this problem, we proposed a neural network to synthesize complete, dense, and uniform point clouds for vehicles from MLS data, named Vehicle Points Completion-Net (VPC-Net). In this network, we introduce a new encoder module to extract global features from the input instance, consisting of a spatial transformer network and point feature enhancement layer. Moreover, a new refiner module is also presented to preserve the vehicle details from inputs and refine the complete outputs with fine-grained information. Given sparse and partial point clouds as inputs, the network can generate complete and realistic vehicle structures and keep the fine-grained details from the partial inputs. We evaluated the proposed VPC-Net in different experiments using synthetic and real-scan datasets and applied the results to 3D vehicle monitoring tasks. Quantitative and qualitative experiments demonstrate the promising performance of the proposed VPC-Net and show state-of-the-art results.