The　extant　literature　mainly　utilized　the　wavelet　tools　and　EMD-type　methods　to　investigate　linkages　between　different　markets　based　on　the　frequency-domain　information,　confronting　the　difficulties　of　the　wavelet　basis　selections　and　scale　aliasing　phenomenon.　To　overcome　these　disadvantages,　the　present　study　proposes　a　BEKK-GARCH-AFD　approach　based　on　the　adaptive-Fourier-decomposition　(AFD)　to　reveal　the　linkages　between　the　international　crude　oil　market　and　the　Chinese　stock　market.　According　to　the　spillover　effect　between　markets　revealed　by　BEKK-GARCH,　the　proposed　approach　could　further　disclose　the　linkages　between　markets　under　external　shocks　with　high-resolution　information　concerning　market　fluctuations　provided　by　the　AFD.　Our　empirical　results　demonstrate　that　the　oil　supply　and　demand　shocks　caused　by　external　events　(e.g.,　the　strikes,　the　geopolitics,　and　the　natural　disasters)　will　put　pressure　on　the　Chinese　stock　market,　while　the　combination　of　bullish　and　bearish　events　(e.g.,　the　reduction　of　crude　oil　production　and　the　shale　oil　boom)　contributes　to　stabilizing　the　stock　market.