Fuzzing is one of the prevailing methods for vulnerability detection. However, even state-of-the-art fuzzing methods become ineffective after some period of time, i.e., the coverage hardly improves as existing methods are ineffective to focus the attention of fuzzing on covering the hard-to-trigger program paths. In other words, they cannot generate inputs that can break the bottleneck due to the fundamental difficulty in capturing the complex relations between the test inputs and program coverage. In particular, existing fuzzers suffer from the following main limitations: 1) lacking an overall analysis of the program to identify the most "rewarding" seeds, and 2) lacking an effective mutation strategy which could continuously select and mutates the more relevant "bytes" of the seeds. In this work, we propose an approach called ATTuzz to address these two issues systematically. First, we propose a lightweight dynamic analysis technique which estimates the "reward" of covering each basic block and selects the most rewarding seeds accordingly. Second, we mutate the selected seeds according to a neural network model which predicts whether a certain "rewarding" block will be covered given certain mutation on certain bytes of a seed. The model is a deep learning model equipped with attention mechanism which is learned and updated periodically whilst fuzzing. Our evaluation shows that ATTuzz significantly outperforms 5 state-of-the-art grey-box fuzzers on 13 popular real-world programs at achieving higher edge coverage and finding new bugs. In particular, ATTuzz achieved 2X edge coverage and 4X bugs detected than AFL over 24-hour runs. Moreover, ATTuzz persistently improves the edge coverage in the long run, i.e., achieving 50% more coverage than AFL in 5 days.