A front vehicle-body structure of a vehicle is provided that allows for lower deceleration (so-called G) for occupants in the event of an oblique collision, which involves the largest load input, while restraining a load in a shear direction from being input to connecting portions of frames. A front vehicle-body structure of a vehicle includes a suspension housing formed with a suspension damper supporting portion, an upper arm supporting portion, and a lower arm supporting portion. A plurality of frames connecting the suspension housing and a vehicle cabin structural member are provided, and at least one frame of the plurality of frames is configured to be facilitated to break in a Z-shape in vehicle plan view in the event of an oblique collision.