Among current anchor-based detectors, a positive anchor box will be intuitively assigned to the object that overlaps it the most. The assigned label to each anchor will directly determine the optimization direction of the corresponding prediction box, including the direction of box regression and category prediction. In our practice of crowded object detection, however, the results show that a positive anchor does not always regress toward the object that overlaps it the most when multiple objects overlap. We name it anchor drift. The anchor drift reflects that the anchor-object matching relation, which is determined by the degree of overlap between anchors and objects, is not always optimal. Conflicts between the fixed matching relation and learned experience in the past training process may cause ambiguous predictions and thus raise the false-positive rate. In this paper, a simple but efficient adaptive two-stage anchor assignment (TSAA) method is proposed. It utilizes the final prediction boxes rather than the fixed anchors to calculate the overlap degree with objects to determine which object to regress for each anchor. The participation of the prediction box makes the anchor-object assignment mechanism adaptive. Extensive experiments are conducted on three classic detectors RetinaNet, Faster-RCNN and YOLOv3 on CrowdHuman and COCO to evaluate the effectiveness of TSAA. The results show that TSAA can significantly improve the detectors' performance without additional computational costs or network structure changes.