In a heat exchanger in which the number of parts is small, assembling is easy, bonded portions of each part are fewer and reliability of brazing is improved, a core body is constituted by turning up and bending a strip-shaped metal plate in a fanfold manner, and first flow passages and second flow passages are formed alternately in the thickness direction. Both ends of each of the first flow passages are blocked by each come tooth of a pair of comb-state members, and a fin is set within the second flow passages so as to constitute a core. And in the heat exchanger in which a cylindrical casing is fitted with the outer periphery of the core body, the comb-state member has its tooth base crossing perpendicularly with each of the comb tooth and a root of each comb tooth bent in the L-shape along the tooth base, the plane of the tooth base is brought into contact with a turned-up end edge, and each connection portion between the comb-state member and the core body is integrally brazed/fixed.