This paper investigates the extreme dependence between the Asia-Pacific stock markets and the international crude oil market by applying the quantile regression theory and using daily data from January 4th, 2000 to July 4th, 2016. The authors obtain a more detailed result on the degree and structure of the dependence, and furthermore, the results present an asymmetric and heterogeneous dependence. Moreover, the dependence increases dramatically after a structural break point, meaning a crisis. Additionally, the authors observe a more significant dependence at the lower tails than the upper tails. They demonstrate the positive relationship at low quantiles, which is evidence of positive dependence in recessions or bearish markets.