A functionally graded membrane (FGM) with a special spiral-structured cellulose acetate (CA) membrane was prepared by electrospinning under different collection distances. The membrane morphology was analyzed by scanning electron microscopy (SEM). FESEM images revealed that the high concentration shows the formation of fibers with an irregular diameter, with a large diameter distribution range. The fiber collected at a short distance of 10 cm experiences the strong electrostatic force, resulting in the short flight time for the polymer jet. This causes the bending instability of the polymer jet forming the comparatively thick fiber diameters, whereas the fiber collected at 15 cm shows the presence of a smooth, homogeneous diameter. Furthermore, the water flux of the membrane was determined using 50 mL of Amicon stirred cells. The fiber collected at different distances showed diameter variation, which is used to design a special spiral structure on the membrane by auto-moving the collector between the fixed distances of 10–20 cm. This technique will reveal a new approach for the fabrication of a special spiral structure on the nanofibrous membrane for different biomedical applications from different polymers. Meanwhile, the fabricated FGM with a special spiral-structure CA membrane demonstrates high water permeation flux.