Disclosed herein is a beam for a bumper. The beam includes: a rail member installed on a body of a vehicle, wherein the rail member is formed by processing a continuous fiber thermoplastics (CFT) into a rail shape and has a coupling portion having a flange-shaped coupling surface; a stay member disposed at the either side portion of the rail member in the longitudinal direction so that it is located between the body and the rail member, wherein the stay member is formed by processing the continuous fiber thermoplastics (CFT) into a stay shape, and is coupled with the rail member such that a coupling surface having a flange shape in parallel with the coupling surface of the coupling portion is coupled with it; and a fastening plate disposed between the coupling portion and the stay member to enhance rigidity of the coupling surface of the stay member.