A bent metal member which is obtained by bending accompanied by heat treatment of a zinc-based coated metal material and which is suitable for use in components of automobiles due to having a high strength and excellent post-painting corrosion resistance is manufactured. The outer surface of a tubular metal material having on its surface a Zn—Fe alloy coating layer with a coating weight of 30-90 g/m2 per side, an Fe content of 8-20%, and a surface roughness Ra of at most 0.8 μm is supported at two locations spaced in the axial direction of the metal material so that the material can move in its axial direction, the metal material is heated between the two locations to a temperature range of at least the Ac3 point at a heating speed such that the rate of temperature increase is at least 3.0×102° C. per second while feeding the metal material in its axial direction, holding so that the length of time for which the surface of the metal material is at 8.0×102° C. or higher is at most 2 seconds, then rapid cooling is carried out, and the position of the downstream of the two locations in the feed direction of the metal material is two-dimensionally or three-dimensionally varied to impart a bending moment to the heated portion of the metal material. A bent metal member having a Zn-based layer which contains an η phase and which has a coating weight of 30-90 g/m2 per side, an Fe content of 8-35%, 35%, and a surface roughness Ra of at most 2.0 μm can be manufactured.