An axial and radial cross flow moving bed adsorption reactor and an activated coke flue gas desulfurization and denitration technology thereof are used for realizing the purposes that SO2, NOx, mercury, dioxin and other pollutants in flue gas are unitedly removed and integrally purified in an adsorption reactor, and belong to the technical field of comprehensive waste flue gas treatment. The adsorption reactor is a combined type double-section double-inverse U-type axial and radial cross flow moving bed, awherein desulfurization area is arranged at a lower section of the axial and radial cross flow moving bed, an annular internal activated coke particle layer and an annular external activated coke particle layer are arranged, and the desulfurization area is divided into a coarse desulfurization area and a fine desulfurization area; a denitration area is arranged at an upper section of the axial and radial cross flow moving bed, and an activated coke particle layer is arranged; an ammonia spray pipe is arranged between the upper section and the lower section; and flue gas is filled along a double-port counter annular gas flow channel structure, the flue gas of the lower section centripetally flows to be desulfurized, and the flue gas of the upper section centrifugally flows to be denitrated. According to the reactor and the technology, desulfurization and denitration are realized in one adsorption reactor, so the adsorption reactor has the advantages of efficient utilization of activated coke, uniform flue gas mixing, sufficient gas-solid contact, stability and reliability in operation, operation cost saving and the like.