The present invention discloses a flue gas dust removal desulfurization reactor and a flue gas desulfurization method. The reactor of the present invention comprises a pre-treatment unit and a deep treatment unit, wherein the two units form an H-shaped double-tower structure, the pre-treatment unit sequentially comprises a flue gas inlet, a turbulent scrubber, a waterdrop-shaped regular packing assembly, and a first-stage liquid holding tank from top to bottom, the deep treatment unit comprises a second-stage liquid holding tank, a packing assembly, a demister assembly and a purified flue gas outlet from bottom to top, and the pre-treatment unit and the deep treatment unit are communicated through the flue gas channel on the middle portion. The reactor of the present invention can achieve functions of one spraying and two-stage absorption/purification, has advantages of high contaminant removal rate, low energy consumption and the like, and is especially suitable for the dust removal desulfurization process of low dust content flue gas.