Structure of polymer fiber membranes plays a vital role in controlling cell responses as applied to immobilize targets for specific cell interactions. Electrospinning is a simple and powerful method to prepare polymer fiber membranes with scales from nano- to micrometers. In this report, a facile yet versatile strategy has been developed for fabricating polymer nanofiber membranes with well-aligned structures using a glass sheet between the needle and a static drum as the collector. Effects of solution concentration, polymer molecular weight, applied voltage, and collection distance on the morphologies of the formed fibers were systematically studied. Adhesion of cells (e.g., mouse melanoma cells B16-F10 and fibroblast cells NIH-3T3) on the fiber membrane has been further investigated. Our results show that cell morphologies varied from elongated to spherical on the random fiber membrane when the pore area of membrane decreased. In contrast, on the membrane with aligned morphology, when decreasing the gap width of fiber membrane, cell is found to keep elongated state and spread along the alignment direction. This work provides a facile yet effective strategy to engineer surface structures of the fiber membranes for controlling cell adhesion.