Object tracking has been broadly applied in unmanned aerial vehicle (UAV) tasks in recent years. However, existing algorithms still face difficulties such as partial occlusion, clutter background, and other challenging visual factors. Inspired by the cutting-edge attention mechanisms, a novel object tracking framework is proposed to leverage multi-level visual attention. Three primary attention, i.e., contextual attention, dimensional attention, and spatiotemporal attention, are integrated into the training and detection stages of correlation filter-based tracking pipeline. Therefore, the proposed tracker is equipped with robust discriminative power against challenging factors while maintaining high operational efficiency in UAV scenarios. Quantitative and qualitative experiments on two well-known benchmarks with 173 challenging UAV video sequences demonstrate the effectiveness of the proposed framework. The proposed tracking algorithm favorably outperforms 12 state-of-the-art methods, yielding 4.8% relative gain in UAVDT and 8.2% relative gain in UAV123@10fps against the baseline tracker while operating at the speed of $\sim$ 28 frames per second.