Developing an abstractive text summarization (ATS) system that is capable of generating concise, appropriate, and plausible summaries for the source documents is a long-term goal of artificial intelligence (AI). Recent advances in ATS are overwhelmingly contributed by deep learning techniques, which have taken the state-of-the-art of ATS to a new level. Despite the significant success of previous methods, generating high-quality and human-like abstractive summaries remains a challenge in practice. The human reading cognition, which is essential for reading comprehension and logical thinking, is still relatively new territory and underexplored in deep neural networks. In this article, we propose a novel Hierarchical Human-like deep neural network for ATS (HH-ATS), inspired by the process of how humans comprehend an article and write the corresponding summary. Specifically, HH-ATS is composed of three primary components (i.e., a knowledge-aware hierarchical attention module, a multitask learning module, and a dual discriminator generative adversarial network), which mimic the three stages of human reading cognition (i.e., rough reading, active reading, and postediting). Experimental results on two benchmark data sets (CNN/Daily Mail and Gigaword) demonstrate that HH-ATS consistently and substantially outperforms the compared methods.