An overflow pipe assembly includes an overflow pipe having an end portion. An adaptor is connected to the end portion of the overflow pipe and includes a first connection portion formed to the center thereof. A second connection portion which is a slot, and a third connection portion which is a bore, are respectively formed to two ends of the adaptor. A cover includes multiple protrusions which are engaged with the engaging portions of the adaptor to connect the cover to the adaptor. When installing the adaptor to an overflow pipe with two tubular parts, the adaptor does not shift by extending bolts through the second and third connection portions and connected to the two tubular parts. When installing the adaptor to an overflow pipe with a single tube, a bolt extends through the first connection portion and is connected to the tube.