Disclosed are a building envelope inner and outer wall anti-seismic and sound insulation anti-cracking integrated structure and a construction method of the structure. An outer wall is connected with the outer side of a frame column to form an integrated building envelope surrounding the frame column, one part of the frame column is embedded in the outer wall, the outer wall is a cast-in-place sandwich wall, the outer wall is filled with light porous inorganic core materials, a lightgage steel joist in the core materials is anchored with face plates on the two sides, the outer wall is connected with the inner wall through connecting ribs, and a reinforcing keel is arranged on the connecting portion. According to the structure, containment and heat preservation are integrated, connection between the cast-in-place light inorganic heat preservation composite outer wall and the constructed inner wall is successfully achieved, the good heat preservation, sound isolation and deformation anti-cracking treatment is achieved, industrial wastes are recycled to be used as raw materials to form nonflammable inorganic foam heat preservation slurry, and due to the rich porous structure in the slurry, the slurry has the excellent heat preservation and sound isolation effects. According to the structure and the method, form removal is not required, construction is easy, the forming speed is high, maintenance is not needed, flexible and continuous casting can be achieved, the building construction efficiency is improved by 30 percent, and the cost is reduced by more than 10 percent.