The fuel efficiency and emission gas regulation of passenger cars are two important issues in these days. The best way to increase the fuel efficiency without sacrificing safety is to employ fibre reinforced composite materials in the body of cars. In this work, a new composite bumper that has two pads at the ends of the bumper was developed. The two pads were designed to hit the front two tyres of the car when the bumper brackets collapsed during collision. The end of the bumper beam was designed to have a tapered section to absorb energy by progressive buckling when the pads hit the rims of wheels after collapsing tyres. The composite bumper beam was made of glass fibre fabric epoxy composite material except the elbow section. The elbow section was made of carbon fibre epoxy composite material to increase bending stiffness. From the static bending test of the prototype composite bumper, it was found that the weight of the composite bumper beam was only 30% that of the steel bumper beam without sacrificing the static bending strength.