Open-World Object Detection (OWOD) extends object detection problem to a realistic and dynamic scenario, where a detection model is required to be capable of detecting both known and unknown objects and incrementally learning newly introduced knowledge. Current OWOD models, such as ORE and OW-DETR, focus on pseudo-labeling regions with high objectness scores as unknowns, whose performance relies heavily on the supervision of known objects. While they can detect the unknowns that exhibit similar features to the known objects, they suffer from a severe label bias problem that they tend to detect all regions (including unknown object regions) that are dissimilar to the known objects as part of the background. To eliminate the label bias, this paper proposes a novel approach that learns an unsupervised discriminative model to recognize true unknown objects from raw pseudo labels generated by unsupervised region proposal methods. The resulting model can be further refined by a classification-free self-training method which iteratively extends pseudo unknown objects to the unlabeled regions. Experimental results show that our method 1) significantly outperforms the prior SOTA in detecting unknown objects while maintaining competitive performance of detecting known object classes on the MS COCO dataset, and 2) achieves better generalization ability on the LVIS and Objects365 datasets.