Crowd counting aims to learn the crowd density distributions and estimate the number of objects (e.g. persons) in images. The perspective effect, which significantly influences the distribution of data points, plays an important role in crowd counting. In this paper, we propose a novel perspective-aware approach called PANet to address the perspective problem. Based on the observation that the size of the objects varies greatly in one image due to the perspective effect, we propose the dynamic receptive fields (DRF) framework. The framework is able to adjust the receptive field by the dilated convolution parameters according to the input image, which helps the model to extract more discriminative features for each local region. Different from most previous works which use Gaussian kernels to generate the density map as the supervised information, we propose the self-distilling supervision (SDS) training method. The ground-truth density maps are refined from the first training stage and the perspective information is distilled to the model in the second stage. The experimental results on ShanghaiTech Part_A and Part_B, UCF_QNRF, and UCF_CC_50 datasets demonstrate that our proposed PANet outperforms the state-of-the-art methods by a large margin.