The invention provides a structure of a connecting joint of an infilled wall and a column of an autoclaved aerated concrete slab and a construction method of the structure. The structure includes a corner structure with the L-shaped cross section, ALC insulation boards, an ALC wallboard and elastic filling materials; the corner structure is provided with two installation parts by forming, a corner portion of the corner structure is formed on the connection portion of the two installation parts, and a tail end portion of the corner structure is formed on the end portions of the two installation parts, and the ALC insulation boards are arranged on vertical faces on the two sides, opposite to each other, of the installation parts of the corner structure and are elastically connected with the corner structure; the ALC wallboard is connected with the tail end portion of the corner structure and the end portions of the ALC insulation boards, and meanwhile gaps are formed between the ALC wallboard and the tail end portion of the corner structure and between the ALC wallboard and end portions of the ALC insulation boards; the gaps are filled with the elastic filling materials so as to connect the ALC wallboard with the corner structure and the ALC insulation boards. The structure and the construction method of the structure solve the technical problem that horizontal deformation of the corner structure causes the damage of a enclosure system.