He admitted he helped China in the design and development of a cryogenic fueling system for space launch vehicles from 2003 to October of 2007.
Shu also admitted that he violated the same law in 2003 by exporting to China military technical information from a document about designing and making a liquid hydrogen tank and pumps, valves, filters and instruments.
Four people were arrested in February in connection with two separate alleged incidents of spying for China, the US justice department said at the time.
A man from California was arrested on charges of stealing trade secrets from aerospace manufacturer Boeing, while three others were held on suspicion of passing classified US documents to China.
The accusations were said to relate to the alleged theft of information on the space shuttle, the C-17 military transport aircraft and the Delta IV rocket.
A Chinese-born US engineer was convicted in May of the attempted theft and export to China of thousands of pages of encrypted military data.
China sent its first man into space in 2003 and followed that with a two-man mission in 2005.
The Shenzhou VII, China's third manned space mission, blasted off from Jiuquan Satellite Launch Centre in northwest China in late September.