There is evidence that the Chinese were aware of a spherical earth by the Han dynasty, depending on how one interprets the huntian theory of Chinese cosmology attributed to Zhang Heng (78–139). In his Ling Xian, Zhang Heng wrote:

The enveloping heavens are like a chicken egg, and the celestial form is round like a crossbow pellet; the earth is like the egg yolk, alone occupying the center.

The passage plausibly implies a spherical earth, which is supported by some historians such as Cheng Yen-tsu. However, this is not the only interpretation of Zhang Heng's huntian cosmology; for example, Tang Ruchan suggests that it refers to a half-spherical or disc-shaped earth. Another passage from the Song dynasty philosopher Zhu Xi (1130–1200) also seems to imply that the earth is round:

The form of heaven and earth is like someone putting two bowls together, holding water within. If they are constantly turned with the hands, the water remains inside without spilling. But if the hands are stopped, the water leaks out.

At the very least, Chinese astronomers were calculating celestial motions under the assumption that the earth was spherical. The phenomena of lunar eclipses was explained by Zhang Heng as the the Moon passing through Earth's umbra or shadow.

However, Chinese cartographers kept portraying the Earth as a flat square (the gaitian cosmological theory) up until the arrival of Jesuit missionaries such as Matteo Ricci (1552–1610)during the Ming dynasty. The idea that the earth is a flat square dates back to the Han dynasty, and is referenced in the mathematical treatise Zhoubi Suanjing:

Turning a carpenter's square creates a circle; combining carpenter's squares forms a square. Squareness belongs to the earth; circularity belongs to heaven. Heaven is round; the earth is square

The earth had long been cartographically portrayed as flat by the time that the Jesuits arrived in China, so many Chinese scholars dismissed Ricci's maps of a spherical earth. One such critic was the philosopher Wang Fuzhi (1619–1692), who had personally met Matteo Ricci and objected to the idea of a round earth on the grounds that "from the Earth's inclines, irregularities, heights, depths, and vastness, it is clear that it has no definite form."

At first, they this may seem contradictory. But in premodern China, advancements in one field of science had little impact on other areas of science. What was understood by Chinese astronomers could be completely ignored by Chinese cartographers. On Chinese science, Nathan Sivin writes:

One aspect was that there does not seem to have been a systematic connection between all the sciences in the minds of the people who did them. They were not integrated under the dominion of philosophy, as schools and universities integrated them in Europe and Islam. They had sciences but no science, no single conception or word for the overarching sum of all of them.

For further reading, see:

Cordell, D.K. Yee, “Taking the World’s Measure: Chinese Maps between Observation and Text”, in J.B. Harley and David Woodward, (Eds.), The History Of Cartography (Chicago: University of Chicago Press, 1994)

Sivin, Nathan. “Why the Scientific Revolution Did Not Take Place in China—or Didn’t It?” Chinese Science 5 (1982): 45-66.