The most important primary source for Zheng He's voyages is the account written by Ma Huan (c.1380-1460), an interpreter who sailed with the Admiral on three of his voyages (1413, 1421, 1431). He compiled his experiences into the Yingya Shenglan or Overall Survey of the Ocean's Shores in 1451. A translation by JVG Mills was published by the Hakluyt Society in 1970 as Ying-yai Sheng-lan, The Overall Survey of the Ocean's Shores (1433) and extracts are available as a scan here.

Histories of Zheng He's journeys also draw on an account by Niccolò di Conti (1395-1469), a Venetian merchant who was in the Indian Ocean at the same time as the Chinese fleet and encountered its ships in Calicut, in his De varietate fortunae. Finally, most accounts of Zheng He also draw on the lengthy travelogue composed by Ibn Battuta (1304-1365), a Moroccan who spent several years in the Indian Ocean. Ibn Battuta was not a contemporary of Zheng He's, however, and so is used to provide context and background.

If you can read Chinese, Xheng He xia Xiyang ziliao hubian (1980-89) is a three-volume collection of Chinese-language source materials covering both the voyages and Ming foreign policy.