To provide a continuous production apparatus and a continuous production method for an aromatic polymer which enable resource conservation, energy conservation, and equipment costs reduction. A continuous production method for an aromatic polymer having an ether bond or an imide bond, the method including: (a) supplying a polymerization solvent and a reaction raw material to a continuous production apparatus including a plurality of reaction vessels; (b) performing a polycondensation reaction in the polymerization solvent in at least one of the reaction vessels to form a reaction mixture; and (c) successively moving the reaction mixture to each of the reaction vessel, the steps (a), (b), and (c) being performed in parallel; wherein an ether bond or an imide bond is formed by the polycondensation reaction; respective gas phase parts of the plurality of reaction vessels communicate with one another; and a pressure of each of the gas phase parts is uniform.