A copper fin material for heat-exchangers is characterized in that, on the surface of Cu or Cu alloy strip, an inner side diffused layer comprising Cu and Zn and a surface side diffused layer provided on the surface side thereof comprising Cu, Zn and elements with a lower diffusion coefficient into Cu than that of Zn is formed. A method of producing the same is characterized in that, after an alloy film comprising Zn and element with a lower diffusion coefficient into Cu than that of Zn is formed on the surface of a Cu or Cu alloy strip, a diffusion treatment is performed under heat so that, on the surface of the Cu or Cu alloy strip, an inner side diffused layer comprising Cu and Zn and a surface side diffused layer provided on the surface side thereof comprising Cu, Zn and elements with a lower diffusion coefficient into Cu than that of Zn are formed. Alternatively, the diffusion treatment under heat is combined with a rolling processing step.