An electrical connector for a composite core conductor and a method of controlling crimping thereof includes a coupling portion and a tubular portion extending from the coupling portion. A conductor has a non-metallic core surrounded by electrically conductive strands and has a connecting portion of the core extending axially beyond the strands. The connecting portion is received in the tubular portion. A crimped portion on the tubular portion radially engages the connecting portion and secures the conductor to the tubular portion. The crimped portion is formed by concave surfaces on internal surfaces of crimping dies. The concave surfaces have different radii of curvature than remaining portions of the internal surfaces.