Today it is so significant to pay attention to the oil price and stock market for the future successful profit of domestic companies in Korea. The purpose of this paper is aimed at analyzing the effects between volatility for international oil price and the stock index on the domestic industries in Korea. It is available to use the model empirically for the dubai oil price and the stock index of the Korean industries. Also this paper studies how much impact the oil price to stock index dividing two periods when the international oil prices go up and down on the world in addition to the whole period from January 2000 to December 2015. In this study literature reviews and empirical methods are both used; The literature reviews are covered with theoretical studies on the relationship between the international oil price, stock markets with the election of variables and its examination in the previous studies. Based on these theories, a model which explains the relationship between stock price indexes by Korean industries and KOSPI (Korea Composite Stock Price Index), as a dependant variable and the independent variables which is proposed as the oil prices, the Time-Varying Volatility of oil prices, the stock index for KOSPI, S&P 500 and seventeen industry in Korea. The analysis is carried out the summary statistics for the whole number of observations for sampling of this study was 4000. This data is gathered by the stock index from the fnguide from Korea, the oil prices from Quandi company from Canada, the exchange rate for the Korean won vs. the United States Dollar from Korean Bank. Also in case of the oil price, the Dubai oil occupied around 80 percentages of imported oils to Korea is used to analyze this study rather the Brent crude from the North sea nearby the UK or the West Texas Intermediate price in the US. Through the empirical analysis, the results attained are as follows; Firstly, it had the unit root tests for stationary relation with Augmented Dickey-Fuller and Phillips-Perron, then it used the logarithmic variables because unit roots were present in variables. It had the stationary data using the level variables. In result, it was rejected the non-stationary null hypothesis, and then it had the stationary data in the time-series analysis because we had not the unit root. Secondly, this study had the vector autoregressive(VAR) model which was a general framework to describe the dynamic interrelationship among stationary variables using the first differences because the time series was stationary. After VAR analysis, this study can know the result that the p-value of the construction industry was less than the 5% significance level during the whole period, and then the stock price index of the construction is the most sensitive industry to dubai oil price. In the end, this study shows the findings to give a useful help of the industrial prediction for the stock market and to understand the relation between the oil price and stock market in Korea.