A carrier unit for carrying boxes includes at least one carrier having multiple holes defined therethrough and two first engaging portions are provided on two insides of each of the holes. Multiple parts boxes are engaged with the holes and each box has a body and a cover which is pivotably connected to the body. The body has two second engaging portions which can be engaged with the first engaging portions when the body is installed in one of the holes. The cover has two protruded portions which contact the carrier when the cover is opened so that the second engaging portions can be disengaged from the first engaging portions.