The invention discloses a central water draining pipe assembly with a balance weight. The central water draining pipe assembly comprises connectors (1), and especially, a soft pipe (2) connected withthe connectors (1) is composed of an inner rubber layer (3), an inner adhesive tape layer (4), a high-strength spring steel wire strengthening layer (5), an outer adhesive tape layer (7), an outer rubber layer (7) and an outer protection layer (8) from interior to exterior. At least one rod type balance weight deviating from a soft pipe shaft is arranged on the soft pipe (2). The central water draining pipe assembly is provided with the uniquely designed rod type balance weight deviating from the soft pipe shaft so that repeated bending, collecting and releasing of the water draining soft pipein processing of repeatedly ascending and descending along with an outer floating roof can have the running track which is basically the same, and the service life of the soft pipe is greatly prolonged.