The electrical connecting device has a cable compartment including spaced inner and outer annular portions. At least one of the top and bottom walls of each annular portion is formed with an annular groove. The portion of compartment other than the portions having annular grooves has a height H1 between the top and bottom walls. The height H1 is substantially equal to the width W of a flexible flat cable. The cable may be formed with projections on its edges. The compartment height H1 may be set between the width of the cable portion with the projections and the width of the cable portion without the projections. Therefore, the connector with high quality and high reliability can prevent an impinging noise from being made by vibration.