This paper investigates the dynamic dependence and risk spillover between BRICS stock returns and different types of oil shocks, combining the Structural VAR model and time-varying copula-GARCH-based CoVaR approach. Our findings indicate that the dependence between BRICS stock returns and oil shocks is time-varying and exhibits different behaviours depending on the shock types in the oil market. In general, the shape of the CoVaRs in each country is comparatively different, depending on its special market situation and domestic policies. There is significant risk spillover from oil-specific demand shock to stock returns in all the BRICS countries. Finally, in Brazil, Russia and India, there is a significant asymmetric effect between upside and downside risk spillover based on oil aggregate demand shock and oil-specific demand shock.