Vehicle Re-Identification (V-ReID) is a crucial research topic in the field of intelligent transportation. However, the quick viewpoint variations in vehicle image could significantly degrades the performances of re-identification. To address this issue, we propose a novel viewpoint-aware V-ReID framework called Viewpoint Modeling with Multi-task learning (VMM) that explicitly models viewpoint variations. Our framework introduces a viewpoint predictor that leverages LiDAR annotations from 3D object detection datasets to automatically generate high-quality viewpoint labels, providing rich supervisory signals for training. This predictor is integrated into a multi-task learning framework that decouples viewpoint features from identity features, ensuring robust viewpoint-invariant feature learning. Experimental results on two challenging V-ReID datasets, VeRI and VeRI-Wild, demonstrate that VMM achieves state-of-the-art performance. Compared to existing methods with similar network scales, VMM improves the mean Average Precision (mAP) by 0.4% and the Cumulative Matching Characteristic (CMC) at rank-1 by 0.12% on the VeRI dataset, and achieves a 0.26% improvement in mAP on the VeRI-Wild dataset.