A universal air pump includes a pump; a head mounted to the pump and having a central hole and an air inlet at a side wall thereof; a cylindrical block pivotably fitted in the central hole of the head and having a central chamber, an annular channel on an outer surface thereof, which faces to the air inlet of the head, and at least one air hole defined through an underside of the annular channel and communicating with the central chamber; a fixing seat having a stub tube engaged with the central chamber of the cylindrical block, and an axially-extended through hole communicating with the central chamber; and an air delivery tube mounted to the fixing seat and communicating with the axially-extended through hole. Thus the air delivery tube can rotate relative to the head so as to allow the air pump to be operated at any angle.