Abstract: The seasonal evolution of the Asian monsoon precipitation is crucial to Asian agricultural production and social economy. Based on the observations, we assess and compare the performance of the latest version of the IAP/LASG Flexible Global Ocean–Atmosphere (FGOALS-g3) with that of FGOALS-g2 in simulating the Asian monsoon seasonal evolution. Compared with an atmospheric experiment driven by historical monthly mean FGOALS-g3 SST, the influence of air–sea coupling on the monsoon seasonal evolution is investigated. Results show that FGOALS-g3 has improved capability to simulate the precipitation annual cycle in South Asia and the Northwest Pacific region, which may be relevant to the atmospheric model, but does not improve in other regions. Compared with FGOALS-g2, the capability to simulate the Northwest Pacific monsoon onset, withdrawal, peak, and duration, Eastern Arabian Sea monsoon withdrawal and duration, and monsoon peak from the Indian Peninsula to the South China Sea are significantly improved in FGOALS-g3. The model’s air–sea coupling can significantly reduce the simulation biases of the annual precipitation cycle in the Northwest Pacific. The delayed bias onset in South Asia and Indochina Peninsula is increased in FGOALS-g3 relative to FGOALS-g2, which is associated with weak Somali jets caused by dry bias in African land in May. In the Northwest Pacific, the bias of monsoon onset simulation (delayed in the west and advanced in the east) is significantly reduced in FGOALS-g3 mainly because the SST bias in the tropical Pacific is improved, and the local Hadley circulation is strengthened, resulting in anomalous subsidence in the region, which reduces the wet bias on the west in January, increases the relative precipitation, and improves the wet bias on the east as a result of compensation between dry biases in May and January. The improvement of the tropical SST pattern in the coupled model has significant implications for improving the simulation of the Asian monsoon precipitation annual cycle.