As we all know, Xiang Yu died in the siege of Gaixia. This battle was the decisive battle in the Chu-Han conflict.

So we only need to find out the time of the Battle of Gaixia.

In December of the fifth year of Emperor Gao of the Han Dynasty (202 BC), during the Chu-Han War, the Chu and Han armies fought a strategic decisive battle at Gaixia (now the north bank of the Tuo River southeast of Lingbi, Anhui).

The Battle of Gaixia broke out in December 202 BC. Therefore, Xiang Yu died in December 202 BC