A high speed transmission connector including several signal contact pairs arranged in a parallel array, each including a pair of signal contacts constituting a balanced transmission line; several ground contacts, each being arranged between two signal contact pairs arranged in the parallel array; and an electro-insulating body supporting the signal contact pairs and the ground contacts. Each signal contact is provided with a contacting section at one longitudinal end for conductive contact with a corresponding signal contact of a counterpart connector, a board connecting section at another longitudinal end for connection with a conductor on a circuit board, and an attaching section between the contacting section and the board connecting section for an attachment to the body. All of the board connecting sections of the signal contacts are disposed along a first lateral surface of the body. The signal contacts of the signal contact pairs are individually covered, at least partially, by materials having dielectric constants different from each other, in certain regions defined between board connecting sections and attaching sections.