An insulation-piercing connector includes a connector body made of an insulating material, and a plurality of contacts made of a resilient conductive metal. Each of the contacts consists of a contact element to be connected to a contact of a mating connector, a fixing element carried by the connector body and a U-shaped piercing terminal element extending from a surface of the connector body and embracing a wire between legs of the U-shaped element. The contacts are arranged staggered in at least two rows. A cover is made of an insulating material and formed with terminal element receiving grooves for receiving the U-shaped elements of the contacts. When the cover is covered onto the connector body, the cover forces wire into the U-shaped elements and embraces the wires between the cover and the connector body. Surfaces of the connector body for embracing the wires in conjunction with the cover are raising inclination surfaces from a side of the U-shaped piercing elements in one row toward above the U-shaped piercing elements in the other row to form alternately reversely inclined surfaces, and surfaces of the cover for embracing the wires are inclination surfaces auxiliary with said alternately inclined surfaces of the connector body.