DNS(direct numerical simulation) and LST(linear stability theory) were employed as tools to study the characteristics of instabilities and transitions in hypersonic boundary layers.The characteristics for flow past a blunt cone in Mach 6 free-stream with 5 half-angle at 2 degree angle of attack (AOA) were analyzed.The results show that there are multi branch instability modes.The instabilities of the blunt cone with the crossflow generated due to AOA is essential different from the cases without the crossflow.The crook in the transition front near the leeward line arises from a transformation between the instability modes.