The explanation for deep neural networks has drawn extensive attention in the deep learning community over the past few years. In this work, we study the visual saliency, a.k.a. visual explanation, to interpret convolutional neural networks. Compared to iteration based saliency methods, single backward pass based saliency methods benefit from faster speed, and they are widely used in downstream visual tasks. Thus, we focus on single backward pass based methods. However, existing methods in this category struggle to successfully produce fine-grained saliency maps concentrating on specific target classes. That said, producing faithful saliency maps satisfying both target-selectiveness and fine-grainedness using a single backward pass is a challenging problem in the field. To mitigate this problem, we revisit the gradient flow inside the network, and find that the entangled semantics and original weights may disturb the propagation of target-relevant saliency. Inspired by those observations, we propose a novel visual saliency method, termed Target-Selective Gradient Backprop (TSGB), which leverages rectification operations to effectively emphasize target classes and further efficiently propagate the saliency to the image space, thereby generating target-selective and fine-grained saliency maps. The proposed TSGB consists of two components, namely, TSGB-Conv and TSGB-FC, which rectify the gradients for convolutional layers and fully-connected layers, respectively. Extensive qualitative and quantitative experiments on the ImageNet and Pascal VOC datasets show that the proposed method achieves more accurate and reliable results than the other competitive methods. Code is available at https://github.com/123fxdx/CNNvisualizationTSGB.