A front vehicle-body structure of a vehicle comprises a front frame which extends in a longitudinal direction, an apron reinforcement which is positioned above and on an outward side, in a vehicle width direction, of the front frame and extends in the longitudinal direction, and a suspension housing which is provided to be laid between the front frame and the apron reinforcement and accommodating a suspension therein, wherein the suspension housing includes a narrow-width portion which has the narrowest width in the longitudinal direction in an upper view, and a suspension tower portion where a damper member of the suspension is attached is formed at a portion of the suspension housing which includes the narrow-width portion.