Purpose: This study investigates the degree and extent of volatility interdependence between the Islamic and conventional stock markets represented by using the Dow Jones indices for the period spanning from Dec 1, 2008, to Dec 31, 2016. Over the last two decades, the stock market has developed rapidly as a new investment instrument and these investments haven't solely extended within the money market and conventional market but also in the developing Islamic markets. Design/Methodology/Approach: GARCH(1,1) conditional volatility series are generated and then further used the Quantile regression approach on volatility series to check the financial markets’ interdependence. Findings: The results show that stock markets are interdependent on all three quantile levels. Accordingly, the structure of interdependence is asymmetric for both Islamic and conventional stock markets. Implications/Originality/Value: Investors, government regulators, and academics can all learn from the findings of this study. The potential for spillover of volatility from conventional stock markets to Islamic stock markets can be effectively countered by investors who develop and implement their unique strategies.