A flat multi-conductor cable connector comprises a main body and a back plate. Arc-shaped cross-section flat-multi-conductor-cable holding grooves extending parallel to each other are formed in the main body and the back plate in a symmetrical manner. The opposing faces of a flat multi-conductor cable are held in the grooves of the main body and the back plate, so that the cable is sandwiched between the main body and the back plate for electric connection between intended conductors of the flat multi-conductor cable and a device mounted on an upper face of the main body. The number of grooves of either of the main body and the back plate is at least one or more greater than the number of poles of the flat multi-conductor cable. Protrusions are provided in middle portions of alternate grooves of the back plate except the two endmost grooves, and block the alternate groove.