A connector for coaxial cables in the form of three flat cables. The coaxial cables are arranged in the cable holder in three rows, so that bared signal conductors extend straight from the cable holder in the insulating body of the connector and ground conductors or ground wires remain in the cable holder. The connector includes wide ground contacts which are inserted in the cable holder to contact the ground conductors or ground wires of the coaxial cables under pressure, and three rows of signal contacts to which bared ends of signal conductors of the coaxial cables are soldered. Three rows of signal contacts are supported by three parallel support plates, respectively. The ground contacts are arranged between first and second rows of the signal contacts and between second and third rows of the signal contacts. A ground shell surrounds the signal contacts whereby a multi-layer strip line structure is formed.