Semiconductor photocatalysis is a promising technology for removing contaminants from water. Particularly, visible-light photocatalysis has attracted much attention because of its potential to utilize solar energy. However, nano-sized visible-light-driven photocatalysts easily aggregate during water treatment. Besides, it is difficult to recycle them from treated systems. Therefore, it is of great importance to develop visible-light-responsive immobilized photocatalysts with high activity. In this work, MWCNTs/Ag₃PO₄/polyacrylonitrile (PAN) ternary composite fiber membranes (TCFMs) with good photocatalytic performance were fabricated by electrospinning technique combined with in situ Ag₃PO₄ forming reaction. Due to the addition of MWCNTs, the band gap of MWCNTs/Ag₃PO₄/PAN TCFMs became narrower than that of Ag₃PO₄/PAN binary composite fiber membranes (BCFMs), which made MWCNTs/Ag₃PO₄/PAN TCFMs be able to use light at longer wavelengths. Compared with Ag3PO4/PAN BCFMs, the as-prepared MWCNTs/Ag₃PO₄/PAN TCFMs showed enhanced photocatalytic activity and stability for degrading rhodamine B (RhB) in batch processing systems, which mainly ascribed to fast electron transfer from Ag₃PO₄ to MWCNTs and the resulting high electron-hole (e^--h⁺) separation efficiency. Radical trapping experiments revealed that holes (h⁺) and superoxide radicals (O2^-) played primary roles in RhB degradation. In addition, the flexible MWCNTs/Ag₃PO₄/PAN TCFMs also showed potential practical application in the continuous wastewater treatment by a suitable photocatalytic membrane reactor. This work provides a facile approach to prepare flexible supported photocatalytic membrane with visible-light response, high activity and good stability.