This paper uses multivariate DCC-GARCH model to investigate the volatility of dynamic correlation between MSCI Taiwan stock index and the USA, China, Japan , Asia and global stock market. The existence of stock market volatility asymmetry, volatility spread of infection and clustering effects also are analysed, while in case of the U.S. sub-prime mortgage crisis and triggered the global financial tsunami. It discusses the Taiwan stock market fluctuations and structural changes in the international markets and the market dynamics related to change of influence and change. The main findings are (1)The volatility of continuity between the spread of infection and the clustering effect between the Taiwan stock market and international market fluctuations, (2) During the global financial tsunami, the correlation between changes in the international market and the market Correlation of different dynamic fluctuations and structural changes occurring in different time point also show the impact of changes of individual markets (3)The correlation between MSCI Taiwan stock index and the USA, China , Japan, indicates that the impact of change of stock the Japanese stock market on the MSCI Taiwan stock index is low, while China and the MSCI Taiwan stock index-related enhances, (4) market structure changes, the MSCI Taiwan stock index and the global dynamic fluctuations in the market is still a significant, The visible impact of the shock oscillation is wide and return to equilibrium of adjustment is still ongoing.