A solution is to produce an acid gas separation composite membrane provided with an acid gas separation facilitated membrane on a porous support, including; arranging of a coating liquid for acid gas separation formed through dispersing or dissolving into water a polyvinyl acetal compound formed through crosslinking, by an acetal bond, block copolymers formed through bonding of a polymer block formed of polyvinyl alcohol and a polymer block formed of polyacrylate through a linking group, an acid gas carrier and at least one kind of anion other than hydroxide ion, carboxyl ion, carbonate ion and bicarbonate ion, and coating of the coating liquid for acid gas separation onto a hydrophobic surface of the porous support having hydrophobicity at least on one surface to form the acid gas separation facilitated transport membrane thereon.