Transmission mechanisms of volatility between two crude oil markets (WTI and Brent markets) have drawn the attention of numerous academics and practitioners because they both play crucial roles in portfolio and risk management in crude oil markets. In this context, we examined the volatility linkages between two representative crude oil markets using a VECM and an asymmetric bivariate GARCH model. First, looking at the return transmission through the VECM test, we found a long-run equilibrium and bidirectional relationship between two crude oil markets. However, the estimation results of the GARCH-BEKK model suggest that there is unidirectional volatility spillover from the WTI market to the Brent market, implying that the WTI market tends to exert influence over the Brent market and not vice versa. Regarding asymmetric volatility transmission, we also found that bad news volatility in the WTI market increases the volatility of the Brent market. Thus, WTI information is transmitted into the Brent market, indicating that the prices of the WTI market seem to lead the prices of the Brent market.