A front vehicle-body structure of a vehicle, the front vehicle-body structure comprising: a floor panel; a side sill extending substantially in a front-rear direction on a vehicle-width-direction outer end portion of the floor panel, wherein a cross-section of the side sill orthogonally intersecting with a front-rear direction is formed as a closed cross-section; a floor frame extending in the front-rear direction on vehicle-width-direction inner side of the side sill, wherein a cross-section of the floor frame orthogonally intersecting with the front-rear direction is formed as a closed cross-section together with the floor panel; a first cross member connecting a front portion of the side sill and the floor frame to each other substantially in a vehicle width direction, wherein a cross-section of the first cross member orthogonally intersecting with the vehicle width direction is formed as a closed cross-section together with the floor panel; and a second cross member positioned on a rear side of the first cross member and connecting the side sill and the floor frame to each other in substantially the vehicle width direction, wherein a cross-section of the second cross member orthogonally intersecting with the vehicle width direction is formed as a closed cross-section together with the floor panel, wherein wherein the floor panel has a quadrilateral closed region surrounded by the side sill, the floor frame, the first cross member, and the second cross member on a periphery of the quadrilateral closed region; characterized by a high-rigidity portion linearly extending in a direction intersecting with a virtual line at an angle of 45 degrees or more in a plan view, the virtual line connecting a front portion on a vehicle-width-direction outer side of the closed region and a rear portion on a vehicle-width-direction inner side of the closed region to each other, and wherein the high-rigidity portion has a higher rigidity than rest of portions provided in the closed region. a floor panel; a side sill extending substantially in a front-rear direction on a vehicle-width-direction outer end portion of the floor panel, wherein a cross-section of the side sill orthogonally intersecting with a front-rear direction is formed as a closed cross-section; a floor frame extending in the front-rear direction on vehicle-width-direction inner side of the side sill, wherein a cross-section of the floor frame orthogonally intersecting with the front-rear direction is formed as a closed cross-section together with the floor panel; a first cross member connecting a front portion of the side sill and the floor frame to each other substantially in a vehicle width direction, wherein a cross-section of the first cross member orthogonally intersecting with the vehicle width direction is formed as a closed cross-section together with the floor panel; and a second cross member positioned on a rear side of the first cross member and connecting the side sill and the floor frame to each other in substantially the vehicle width direction, wherein a cross-section of the second cross member orthogonally intersecting with the vehicle width direction is formed as a closed cross-section together with the floor panel, wherein wherein the floor panel has a quadrilateral closed region surrounded by the side sill, the floor frame, the first cross member, and the second cross member on a periphery of the quadrilateral closed region; characterized by a high-rigidity portion linearly extending in a direction intersecting with a virtual line at an angle of 45 degrees or more in a plan view, the virtual line connecting a front portion on a vehicle-width-direction outer side of the closed region and a rear portion on a vehicle-width-direction inner side of the closed region to each other, and wherein the high-rigidity portion has a higher rigidity than rest of portions provided in the closed region.