The invention discloses a consecutive reaction apparatus for moisture sludge through anhydration and pyrolysis under microwave irradiation as well as a method thereof. The condensation comprises a sludge warehouse, a stirrer, a hopper feeder, a sludge-shaped controller, a belt sender, a power control microwave irradiation device, a microwave pyrolysis reaction chamber, a pressure sensing controller, a blower fan, a condensation heat exchanger, a scraper plate separator, an oil-water separating device, a liquid dredging groove, a coke storage tank, a product oil tank, a product gas tank, a nitrogen generator, a coke crusher, a sludge water pot and a gas shunting plate. According to the invention, microwave material internal heating characteristic can be fully used for reducing heat radiation loss, moisture sludge is directly performed with anhydration and pyrolysis to obtain the cracking oil, combustible gas and solid coke; heat recovery of the product gas and auxiliary microwave heating characteristic of the products residue are fully used for reducing the operation cost, and sludge pyrolysis efficiency and products quality can be increased. The apparatus has the advantages of simple structure, small volume, reasonable design and convenient market popularization, and is suitable for industrial application of microwave sludge continuous pyrolysis.