MOBA games, e.g., Honor of Kings, League of Legends, and Dota 2, pose grand challenges to AI systems such as multi-agent, enormous state-action space, complex action control, etc. Developing AI for playing MOBA games has raised much attention accordingly. However, existing work falls short in handling the raw game complexity caused by the explosion of agent combinations, i.e., lineups, when expanding the hero pool in case that OpenAI's Dota AI limits the play to a pool of only 17 heroes. As a result, full MOBA games without restrictions are far from being mastered by any existing AI system. In this paper, we propose a MOBA AI learning paradigm that methodologically enables playing full MOBA games with deep reinforcement learning. Specifically, we develop a combination of novel and existing learning techniques, including off-policy adaption, multi-head value estimation, curriculum self-play learning, policy distillation, and Monte-Carlo tree-search, in training and playing a large pool of heroes, meanwhile addressing the scalability issue skillfully. Tested on Honor of Kings, a popular MOBA game, we show how to build superhuman AI agents that can defeat top esports players. The superiority of our AI is demonstrated by the first large-scale performance test of MOBA AI agent in the literature.