Object detection with transformers (DETR) reaches competitive performance with Faster R-CNN via a transformer encoder-decoder architecture. Inspired by the great success of pre-training transformers in natural language processing, we propose a pretext task named random query patch detection to unsupervisedly pre-train DETR (UP-DETR) for object detection. Specifically, we randomly crop patches from the given image and then feed them as queries to the decoder. The model is pre-trained to detect these query patches from the original image. During the pre-training, we address two critical issues: multi-task learning and multi-query localization. (1) To trade-off multi-task learning of classification and localization in the pretext task, we freeze the CNN backbone and propose a patch feature reconstruction branch which is jointly optimized with patch detection. (2) To perform multi-query localization, we introduce UP-DETR from single-query patch and extend it to multi-query patches with object query shuffle and attention mask. In our experiments, UP-DETR significantly boosts the performance of DETR with faster convergence and higher precision on PASCAL VOC and COCO datasets. The code will be available soon.