The research discusses the interaction between the Stock Index in Taiwan and Exchange Rate such as US dollars, Euro, Renminbi, Japanese Yen, and Hong Kong dollars. Our data comes from Taiwan Economic Journal (TEJ). It concludes the closing price of the Taiwan Stock Exchange Weighted Indices and the spot exchange rate of Taiwan bank. The period of time is from Jan 5 1999 to Oct 30 2015. Our study uses Cointegration Test and perceives there is a long and stable relationship between the Stock Index in Taiwan and the Exchange Rate. Furthermore, we use causality test to test the lead and lag relationship between the Stock Index in Taiwan and the Exchange Rate. To understand the relationship through time passing, we use DCC-GARCH to find the conditional correlation to see the change of the interaction.