She finished eleventh at the 1984 Summer Olympics, and also won the 1984 Friendship Games.

In 1983 she reached the final of the inaugural World Championships in Athletics, but finished 18th and last with only 1.80 metres.

In 1978 she jumped 1.88 m to improve the record with 10 centimetres; in 1982 she jumped 1.89 m. At the 1986 Asian Games Zheng got the silver medal despite equalling the CR, as the winner Megumi Sato, too equalling the CR, achieved the result with fewer failed attempts.

In 1990 Sato set the current Asian Games record with 1.94 m.[2] Her personal best jump was 1.95 metres, achieved in May 1987 in Fukuoka.

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