A smart tree-like nanofiber membrane with pH-responsivity was successfully fabricated by electrospinning poly (vinylidene fluoride)-graft-poly(acrylic acid) (PVDF-g-PAA). X-ray photoelectron spectroscopy, field emission scanning electron microscopy, Fourier transform infrared spectroscopy, and Brunauer-Emmett-Teller surface area measurement were employed to study the molecular structure and morphology of membranes. Through realizing protonation and deprotonation in response to the pH of the aqueous media, the as-prepared membrane is able to alter its wettability and conformation, resulting in the switchable surface oil/water wettability in the aqueous media. More importantly, the as-prepared membrane realized on-demand oil/water separation using gravity alone by switching the pH of the medium. Both separations exhibited excellent efficiency and flux which were attributed to the tree-like structure of the membrane. We believed that this smart membrane with such excellent controllable permeation has potential to be used for several applications, such as water purification, oil recovery and some separation systems.