Thermal InfraRed (TIR) target trackers are easy to be interfered by similar objects, while susceptible to the influence of the target occlusion. To solve these problems, we propose a structural target-aware model (STAMT) for the thermal infrared target tracking tasks. Specifically, the proposed STAMT tracker can learn a target-aware model, which can add more attention to the target area to accurately identify the target from similar objects. In addition, considering the situation that the target is partially occluded in the tracking process, a structural weight model is proposed to locate the target through the unoccluded reliable target part. Ablation studies show the effectiveness of each component in the proposed tracker. Without bells and whistles, the experimental results demonstrate that our STAMT tracker performs favorably against state-of-the-art trackers on PTB-TIR and LSOTB-TIR datasets.