This article used A-share index and H-share index investigates the information transmission mechanism and the home bias hypothesis based on PT/GG model and VECM-BEKK-(BV) GARCH model. The evidence suggests that, in short term, there is a significant innovation shock and unidirectional information transmission from A-share market to H-share market, and unidirectional volatility spillover from H-share to A-share; in long term, A-share market makes primary contribution to the price discovery, and the proportion is 67.94%. The empirical results show that the ”domestic” market can incorporate into new information more efficiently. A-share market is easily considered as the leading market on the aspect of information transmission of returns. Because of exchange risk and political risk, etc., the volatility transmission is from H-share market to A-share market. The conclusion also demonstrates the evidence of the ”home bias hypothesis”.