Local damage of the pipe-ball joints in the grid structure poses a significant safety hazard. Such local damage will be aggravated under uneven snow cover caused by wind-induced snow drifting, eventually leading to partial structural failure. Therefore, it is necessary to analyze the degradation of the structure with local damage under the action of uneven snow load. The CFD numerical simulation technology is adopted to analyze the variation of uneven snow distribution on the roof of an orthogonal quadrangular grid structure under the continuous snowfall for 24 hours at the 90°wind direction and 12m/s wind speed. Then a multi-scale numerical model is established to characterize the crack damage at the pipe-ball joints of the grid structure, and the local damage deterioration degree of the grid structure caused by uneven snow cover is analyzed when there is local damage of different crack sizes at the joints of the grid structure. The results show that the uneven degree of the wind-induced snow cover on the grid structure is very significant, and when there are local crack damages at the pipe-ball joints of the grid structure, most of the joints with damage have different degrees of crack propagation in the middle and late stages of snowfall. The maximum crack propagation is 15.64 mm when the joint damage is the penetrating cracks with the most unfavorable distribution. It indicates that under the extreme load of continuous heavy snowfall, the local damages in the grid structure with existing cracks will be further aggravated, endangering the service safety of the structure.