Object detection is an essential technique for autonomous driving. The performance of an object detector significantly degrades if the weather of the training images is different from that of test images. Domain adaptation can be used to address the domain shift problem so as to improve the robustness of an object detector. However, most existing domain adaptation methods either handle single target domain or require domain labels. We propose a novel unsupervised domain classification method which can be used to generalize single-target domain adaptation methods to multi-target domains, and design a weather-invariant object detector training framework based on it. We conduct the experiments on Cityscapes dataset and its synthetic variants, i.e. foggy, rainy, and night. The experimental results show that the object detector trained by our proposed method realizes robust object detection under different weather conditions.