Factors, such as rapid relative motion, clutter background, etc., make robust small aerial target detection for airborne infrared detection systems a challenge. Existing methods are facing difficulties when dealing with such cases. We consider that a continuous and smooth trajectory is critical in boosting small infrared aerial target detection performance. A simple and effective small aerial target detection method for airborne infrared detection system using light gradient boosting model (LightGBM) and trajectory constraints is proposed in this article. First, we simply formulate target candidate detection as a binary classification problem. Target candidates in every individual frame are detected via interesting pixel detection and a trained LightGBM model. Then, the local smoothness and global continuous characteristic of the target trajectory are modeled as short-strict and long-loose constraints. The trajectory constraints are used efficiently for detecting the true small infrared aerial targets from numerous target candidates. Experiments on public datasets demonstrate that the proposed method performs better than other existing methods. Furthermore, a public dataset for small aerial target detection in airborne infrared detection systems is constructed. To the best of our knowledge, this dataset has the largest data scale and richest scene types within this field.