The invention relates to a flue gas deep desulfurization method of a magnesium strengthened red mud. The raw material red mud is preimpregnated by magnesium desulfurization circulating fluid, and thick red mud preimpregnated slurry and red mud preimpregnated clear liquid are obtained after settling and used as flue gas desulfurization slurry and deep desulfurization liquid respectively; pre-baked anode calcination flue gas enters a desulfurizing tower for spray washing treatment after waste heat recovery, the flue gas firstly passes by a pre-desulfurization area of the lower part of the desulfurizing tower for reverse contact absorption with the red mud preimpregnated slurry, and 80%-90% of SO2 in the flue gas is removed in the area; then the flue gas passes by a partition tower plate and a deep desulfurization area, and the deep desulfurization purpose is realized by the aid of reverse contact absorption of the flue gas with the red mud preimpregnated clear liquid; finally, the flue gas is exhausted out of the desulfurizing tower after the flue gas passes by the upper layer efficient mist removal area of the desulfurizing tower and mist is removed, and standard emission is realized. Compared with the prior art, deep desulfurization and red mud resource comprehensive utilization can be realized simultaneously, the desulphurization efficiency is high, red mud dealkalization is thorough, and the energy consumption is low.