A front vehicle-body structure for a vehicle, comprising: a pair of front frames provided to be separated, in a vehicle width direction, from each other and extending in a vehicle longitudinal direction; a pair of crash cans fixed to respective front ends of the pair of front frames and extending in the vehicle longitudinal direction; and a bumper beam fixed to respective front ends of the pair of crash cans and extending in the vehicle width direction, wherein the bumper beam comprises crash-can fixation portions which are respectively fixed to the pair of crash cans and extension portions which respectively extend outwardly, in the vehicle width direction, from the crash-can fixation portions, each of the pair of crash cans comprises an upper face portion which extends in the vehicle longitudinal direction and forms an upper face of the crash can in a vehicle elevational view, a lower face portion which extends in the vehicle longitudinal direction and forms a lower face of the crash can in the vehicle elevational view, a pair of side face portions which respectively interconnect both end portions, in the vehicle width direction, of the upper face portion and the lower face portion, corner portions which are respectively positioned between the side face portion and the upper face portion and between the side face portion and the lower face portion, a first fragile portion which is provided at each of the corner portions, and a second fragile portion which is provided at at least one of the upper face portion, the lower face portion, and the pair of side face portions, the first fragile portion is configured to be deformed before the second fragile portion when a collision load which is applied toward a vehicle rearward side is inputted to the extension portion of the bumper beam, the second fragile portion is configured to be deformed before the front frame when the collision load applied toward the vehicle rearward side is inputted to the extension portion of the bumper beam, the second fragile portion extends continuously from the first fragile portion in the vehicle width direction and/or in a vertical direction along at least one of the upper face portion, the lower face portion, and the side face portions, the first fragile portion is made of a first bead which is configured such that the corner portion of the crash can is partially recessed, the second fragile portion is made of a second bead which is configured such that the at least one of the upper face portion, the lower face portion, and the pair of side face portions of the crash can is partially recessed, a depth of the first bead is greater than that of the second bead, and a width, in the vehicle longitudinal direction, of the first bead is greater than that of the second bead. a pair of front frames provided to be separated, in a vehicle width direction, from each other and extending in a vehicle longitudinal direction; a pair of crash cans fixed to respective front ends of the pair of front frames and extending in the vehicle longitudinal direction; and a bumper beam fixed to respective front ends of the pair of crash cans and extending in the vehicle width direction, wherein the bumper beam comprises crash-can fixation portions which are respectively fixed to the pair of crash cans and extension portions which respectively extend outwardly, in the vehicle width direction, from the crash-can fixation portions, each of the pair of crash cans comprises an upper face portion which extends in the vehicle longitudinal direction and forms an upper face of the crash can in a vehicle elevational view, a lower face portion which extends in the vehicle longitudinal direction and forms a lower face of the crash can in the vehicle elevational view, a pair of side face portions which respectively interconnect both end portions, in the vehicle width direction, of the upper face portion and the lower face portion, corner portions which are respectively positioned between the side face portion and the upper face portion and between the side face portion and the lower face portion, a first fragile portion which is provided at each of the corner portions, and a second fragile portion which is provided at at least one of the upper face portion, the lower face portion, and the pair of side face portions, the first fragile portion is configured to be deformed before the second fragile portion when a collision load which is applied toward a vehicle rearward side is inputted to the extension portion of the bumper beam, the second fragile portion is configured to be deformed before the front frame when the collision load applied toward the vehicle rearward side is inputted to the extension portion of the bumper beam, the second fragile portion extends continuously from the first fragile portion in the vehicle width direction and/or in a vertical direction along at least one of the upper face portion, the lower face portion, and the side face portions, the first fragile portion is made of a first bead which is configured such that the corner portion of the crash can is partially recessed, the second fragile portion is made of a second bead which is configured such that the at least one of the upper face portion, the lower face portion, and the pair of side face portions of the crash can is partially recessed, a depth of the first bead is greater than that of the second bead, and a width, in the vehicle longitudinal direction, of the first bead is greater than that of the second bead.