Network pruning can significantly reduce the computation and memory footprint of large neural networks. To achieve a good trade-off between model size and performance, popular pruning techniques usually rely on hand-crafted heuristics and require manually setting the compression ratio for each layer. This process is typically time-consuming and requires expert knowledge to achieve good results. In this paper, we propose NAP, a unified and automatic pruning framework for both fine-grained and structured pruning. It can find out unimportant components of a network and automatically decide appropriate compression ratios for different layers, based on a theoretically sound criterion. Towards this goal, NAP uses an efficient approximation of the Hessian for evaluating the importances of components, based on a Kronecker-factored Approximate Curvature method. Despite its simpleness to use, NAP outperforms previous pruning methods by large margins. For fine-grained pruning, NAP can compress AlexNet and VGG16 by 25x, and ResNet-50 by 6.7x without loss in accuracy on ImageNet. For structured pruning (e.g. channel pruning), it can reduce flops of VGG16 by 5.4x and ResNet-50 by 2.3x with only 1% accuracy drop. More importantly, this method is almost free from hyper-parameter tuning and requires no expert knowledge. You can start NAP and then take a nap!