Object detection, as a fundamental computer vision task, has achieved a remarkable progress with the emergence of deep neural networks. Nevertheless, few works explore the adversarial robustness of object detectors to resist adversarial attacks for practical applications in various real-world scenarios. Detectors have been greatly challenged by unnoticeable perturbation, with sharp performance drop on clean images and extremely poor performance on adversarial images. In this work, we empirically explore the model training for adversarial robustness in object detection, which greatly attributes to the conflict between learning clean images and adversarial images. To mitigate this issue, we propose a Robust Detector (RobustDet) based on adversarially-aware convolution to disentangle gradients for model learning on clean and adversarial images. RobustDet also employs the Adversarial Image Discriminator (AID) and Consistent Features with Reconstruction (CFR) to ensure a reliable robustness. Extensive experiments on PASCAL VOC and MS-COCO demonstrate that our model effectively disentangles gradients and significantly enhances the detection robustness with maintaining the detection ability on clean images.