Weakly Supervised Object Localization (WSOL) aims to learn object locations in a given image while only using image-level annotations. For highlighting the whole object regions instead of the discriminative parts, previous works often attempt to train classification model for both classification and localization tasks. However, it is hard to achieve a good tradeoff between the two tasks, if only classification labels are employed for training on a single classification model. In addition, all of recent works just perform localization based on the last convolutional layer of classification model, ignoring the localization ability of other layers. In this work, we propose an offline framework to achieve precise localization on any convolutional layer of a classification model by exploiting two kinds of gradients, called Dual-Gradients Localization (DGL) framework. DGL framework is developed based on two branches: 1) Pixel-level Class Selection, leveraging gradients of the target class to identify the correlation ratio of pixels to the target class within any convolutional feature maps, and 2) Class-aware Enhanced Maps, utilizing gradients of classification loss function to mine entire target object regions, which would not damage classification performance. Extensive experiments on public ILSVRC and CUB-200-2011 datasets show the effectiveness of the proposed DGL framework. Especially, our DGL obtains a new state-of-the-art Top-1 localization error of 43.55% on the ILSVRC benchmark.