Geomagnetic disturbances will induce Geomagnetically Induced Current (GIC) in high voltage power grid, which will cause cascading failure in power grid, resulting in power system collapse or blackout. Therefore, research on risk assessment of cascading failure in power grid under geomagnetic storms can provide important reference for preventing accidents caused by geomagnetic storms. This paper analyzes the mechanism of cascading failure under geomagnetic storm conditions and proposes a risk assessment process for cascading failure in power grid under geomagnetic storms. The process can identify the vulnerable links of the power grid under each geomagnetic storm condition, evaluate the risk of the different stages of the vulnerable links by using the load shedding of the power system and use the critical load shedding caused by vulnerable links to evaluate its risk to the power system. Finally, the proposed process is verified by using the IEEE-RTS79 system. The verification results show the feasibility and validity of the proposed process. The results obtained can provide a reference for quantifying and preventing the risk of the power grid under geomagnetic storm conditions.