Open world object detection aims at detecting objects that are absent in the object classes of the training data as unknown objects without explicit supervision. Furthermore, the exact classes of the unknown objects must be identified without catastrophic forgetting of the previous known classes when the corresponding annotations of unknown objects are given incrementally. In this paper, we propose a two-stage training approach named Open World DETR for open world object detection based on Deformable DETR. In the first stage, we pre-train a model on the current annotated data to detect objects from the current known classes, and concurrently train an additional binary classifier to classify predictions into foreground or background classes. This helps the model to build an unbiased feature representations that can facilitate the detection of unknown classes in subsequent process. In the second stage, we fine-tune the class-specific components of the model with a multi-view self-labeling strategy and a consistency constraint. Furthermore, we alleviate catastrophic forgetting when the annotations of the unknown classes becomes available incrementally by using knowledge distillation and exemplar replay. Experimental results on PASCAL VOC and MS-COCO show that our proposed method outperforms other state-of-the-art open world object detection methods by a large margin.