A panel member having a U-shaped cross section includes step portions at an upper face portion and a lower face portion, and a distance, in a vehicle longitudinal direction, of the step potions from a panel member formed substantially in a flat-plate shape, is configured such that the distance at a central portion, in the vehicle width direction, of a bumper reinforcement is the maximum and the distance decreases gradually toward an outward direction of the vehicle. Accordingly, the vehicle-body structure which can properly ensure the bending strength and also attain the light weight of the bumper reinforcement, improving the load transmission from the bumper reinforcement to crash cans, can be provided.