Despite significant efforts made so far for Weakly Supervised Object Detection (WSOD), proposal generation and proposal selection are still two major challenges. In this paper, we focus on addressing the two challenges by generating and selecting high-quality proposals. To be specific, for proposal generation, we combine selective search and a Gradient-weighted Class Activation Mapping (Grad-CAM) based technique to generate more proposals having higher Intersection-Over-Union (IOU) with ground truth boxes than those obtained by greedy search approaches, which can better envelop the entire objects. As regards proposal selection, for each object class, we choose as many confident positive proposals as possible and meanwhile only select class-specific hard negatives to focus training on more discriminative negative proposals by up-weighting their losses, which can make training more effective. The proposed proposal generation and proposal selection approaches are generic and thus can be broadly applied to many WSOD methods. In this work, we unify them into the framework of Online Instance Classifier Refinement (OICR). Experimental results on the PASCAL VOC 2007 and 2012 datasets and MS COCO dataset demonstrate that our method significantly improves the baseline method OICR by large margins (13.4% mAP and 11.6% CorLoc gains on the VOC 2007 dataset, 15.0% mAP and 8.9% CorLoc gains on the VOC 2012 dataset, and 6.4% mAP and 5.0% CorLoc gains on the COCO dataset) and achieves the state-of-the-art results compared with existing methods.