Multiple object tracking (MOT) constitutes a critical research area within the field of computer vision. The creation of robust and efficient systems, which can approximate the mechanisms of human vision, is essential to enhance the efficacy of multiple object-tracking techniques. However, obstacles such as repetitive target appearances and frequent occlusions cause considerable inaccuracies or omissions in detection. Following the updating of these inaccurate observations into the tracklet, the effectiveness of the tracking model, employing appearance features, declines significantly. This paper introduces a novel method of multiple object tracking, employing graph attention networks and track management (GATM). Utilizing a graph attention network, an attention mechanism is employed to capture the relationships of nodes within the graph as well as node-to-node correlations across graphs. This mechanism allows selective focus on the features of advantageous nodes and enhances discriminability between node features, subsequently improving the performance and robustness of multiple object tracking. Simultaneously, we categorize distinct tracklet states and introduce an efficient track management method, which employs varying processing techniques for tracklets in diverse states. This method can manage occluded tracks in crowded scenes and improves tracking accuracy. Experiments conducted on three challenging public datasets (MOT16, MOT17, and MOT20) demonstrate that our method could deliver competitive performance.