The box includes a case in which heat generating electrical parts are to be arranged. The case has a number of receiving devices for accommodating cooling device with a heat absorbing side inside the case and a heat radiating side outside the case. Even if the arrangement of heat generating electrical parts (7) or a position where the electrical connection box is mounted on a vehicle is changed, the heat generating electrical parts (7) can be cooled by selecting suitable concave grooves (3a) and installing heat pipes (8) id the selected concave (3a).
