The Chinese stock market has developed rapidly since early 1990s, when the two stock exchanges, the Shanghai Securities Exchange and the Shenzhen Securities Exchange, were established. Until 2000, the number of listed domestic companies has reached over 1000, and market capitalization relative to GDP reached about 33.4%. As China joins WTO, the Chinese stock market will become a great concern of the global investors, and will play a more important role in the world economy. The purpose of this paper is to provide an up-to-data account of the Chinese stock exchange market and to test its efficiency. The daily data of the Shanghai Stock Exchange index and eight shares listed in the Shanghai Stock Exchanges are examined, for this purpose. The testing procedure involves three processes: (1) use the Durbin-Watson test, Durbin 'h' test, the Lagrange Multiplier test for autocorrelation to examine the assumption of the model that the successive occurrences are independent; (2) use the Dickey-Fuller tests for unit root to test the assumption that the occurrences are identically distributed; (3) use ARCH test to examine whether the residuals contain some hidden, possibly non-linear structure, and fit a GARCH-M(1,1) model to the first difference if the ARCH effect is found to be present in the share prices.