A low profile connector for a coaxial cable, which includes a metal shell (1) with a cable gripper (3) extending from a side thereof for gripping the coaxial cable; a dielectric block (2) fitted into the metal shell and having a partition wall (4) for defining a contact recess (5) and a connection recess (6); and a U-shaped contact element (10) with a pair of leg members (11, 12) fitted into the contact and connection recesses, respectively, such that a leg member with a connection slit (12A) bites into a dielectric body of the coaxial cable and comes into contact with a central conductor by an insulation replacement technique while the other leg member is supported by the partition wall for contact with a contact element of a mating connector.