This paper studies the price-discovery process for a number of Chinese stocks cross-listed in Shanghai and Hong Kong (SH-HK stocks) in the two periods before and after the Shanghai-Hong Kong Stock Connect, which has greatly eliminated the ownership restriction of A-H shares and liberalized the stock markets in China. Since the Connect enables investors in each market to trade shares listed in the other market by using their local brokers and clearing houses, which also changes the set of investors that participate in each market, it is reasonable to expect that the information incorporated in A-H prices may also change. Indeed, there exists a significant structural change in the AH premium index that coincides with the implementation of the Connect. We use two measures to determine each market's relative contribution to price discovery: common factor weights from Gonzalo and Granger's (1995) permanent transitory model (PT model) and information shares (IS model) defined by Hasbrouck's (1995). We find that for SH-HK stocks, the SH and HK markets do not contribute equally to the price discovery process. Measured by common factor weight, on average HK market contributes 78.6% (91.4%) to price discovery before (after) the Connect. Using information share as measurement, HK market's average contribution is 73.2% (76.3%) before (after) the Connect. The t-tests suggest that the average common factor weight and information share of HK market are significantly greater than 50%, suggesting that the HK market contributes substantially more in the price discovery process. A possible explanation for this finding is that most firms list their H shares earlier than A shares, thus H share price may serve as a reference when A shares become listed and traded, which leads to a greater weight of H share price in the common factor. As the Connect only affects SH-HK stocks, I also use stocks cross-listed in Shenzhen and Hong Kong (SZ-HK stocks) as the control group to analyze the influence of the Connect on each market's relative contribution to price discovery. The results show that on average, the Connect increases the information share of SH market by 17.4%. The economic meaning is that when the better informed investors in HK market trade A shares in SH market through the Connect, the A share price will incorporate more information, which will improve SH market's relative contribution to price discovery. The implication is that the liberalization of an emerging stock market to investors from a developed market will improve its function in price discovery.