The development of deep reinforcement learning (DRL) has benefited from the emergency of a variety type of game environments where new challenging problems are proposed and new algorithms can be tested safely and quickly, such as Board games, RTS, FPS, and MOBA games. However, many existing environments lack complexity and flexibility and assume the actions are synchronously executed in multi-agent settings, which become less valuable. We introduce the Fever Basketball game, a novel reinforcement learning environment where agents are trained to play basketball game. It is a complex and challenging environment that supports multiple characters, multiple positions, and both the single-agent and multi-agent player control modes. In addition, to better simulate real-world basketball games, the execution time of actions differs among players, which makes Fever Basketball a novel asynchronized environment. We evaluate commonly used multi-agent algorithms of both independent learners and joint-action learners in three game scenarios with varying difficulties, and heuristically propose two baseline methods to diminish the extra non-stationarity brought by asynchronism in Fever Basketball Benchmarks. Besides, we propose an integrated curricula training (ICT) framework to better handle Fever Basketball problems, which includes several game-rule based cascading curricula learners and a coordination curricula switcher focusing on enhancing coordination within the team. The results show that the game remains challenging and can be used as a benchmark environment for studies like long-time horizon, sparse rewards, credit assignment, and non-stationarity, etc. in multi-agent settings.