A front vehicle-body structure of a vehicle, comprising: a dash panel partitioning a vehicle room from an engine room at a front vehicle body; a front side frame connected to a front side of the dash panel and substantially extending in a vehicle longitudinal direction, part of which is deformed so as to substantially bend outwardly, in a vehicle width direction, by a collision load in a vehicle frontal collision, the front side frame comprising a front frame which has a closed cross section and which substantially extends in the vehicle longitudinal direction, and a rear frame which forms a closed cross section together with the dash panel and a floor panel, wherein a rear end of the rear frame is joined to the dash panel, and a rear end of the front frame is joined to a front end portion of the rear frame; a sub frame to be provided at a lower portion of the front vehicle body and joined to the front side frame; a reinforcement ( 15; 115) to be provided inside the closed cross section of the front side frame; and a suspension tower joined to said front side frame; wherein a front portion of the reinforcement ( 15; 115) is to be located at a position which corresponds to a bending portion of said front side frame which is to be deformed so as to bend outwardly, in the vehicle width direction, by the collision load in the vehicle frontal collision, wherein said bending portion of the front side frame is provided in front of a joint portion of the front side frame to said suspension tower, and wherein said front side frame is configured so that a second bending portion thereof which is located in back of said bending portion bending outwardly and in front of a connection portion thereof to said dash panel is deformed so as to bend, in the vehicle width direction, by the collision load in the vehicle frontal collision, and a rear portion of said reinforcement ( 15; 115) is located at another position which corresponds to said second bending portion; characterized in that said sub frame is joined via the reinforcement (15; 115) to the front side frame near said joint portion such that the reinforcement (15; 115) is joined to the front frame of the front side frame, wherein a valley portion used as a point causing the bending deformation of the front side frame at its bending portion is formed at a border portion ( α) between a front flat-face portion and a protruding curve portion which are formed at the suspension tower. a dash panel partitioning a vehicle room from an engine room at a front vehicle body; a front side frame connected to a front side of the dash panel and substantially extending in a vehicle longitudinal direction, part of which is deformed so as to substantially bend outwardly, in a vehicle width direction, by a collision load in a vehicle frontal collision, the front side frame comprising a front frame which has a closed cross section and which substantially extends in the vehicle longitudinal direction, and a rear frame which forms a closed cross section together with the dash panel and a floor panel, wherein a rear end of the rear frame is joined to the dash panel, and a rear end of the front frame is joined to a front end portion of the rear frame; a sub frame to be provided at a lower portion of the front vehicle body and joined to the front side frame; a reinforcement ( 15; 115) to be provided inside the closed cross section of the front side frame; and a suspension tower joined to said front side frame; wherein a front portion of the reinforcement ( 15; 115) is to be located at a position which corresponds to a bending portion of said front side frame which is to be deformed so as to bend outwardly, in the vehicle width direction, by the collision load in the vehicle frontal collision, wherein said bending portion of the front side frame is provided in front of a joint portion of the front side frame to said suspension tower, and wherein said front side frame is configured so that a second bending portion thereof which is located in back of said bending portion bending outwardly and in front of a connection portion thereof to said dash panel is deformed so as to bend, in the vehicle width direction, by the collision load in the vehicle frontal collision, and a rear portion of said reinforcement ( 15; 115) is located at another position which corresponds to said second bending portion; characterized in that said sub frame is joined via the reinforcement (15; 115) to the front side frame near said joint portion such that the reinforcement (15; 115) is joined to the front frame of the front side frame, wherein a valley portion used as a point causing the bending deformation of the front side frame at its bending portion is formed at a border portion ( α) between a front flat-face portion and a protruding curve portion which are formed at the suspension tower.