Nanofibres having a parallel line surface texture were electrospun from cellulose acetate butyrate solutions using a solvent mixture of acetone and N,N'-dimethylacetamide. The formation mechanism of the unusual surface feature was explored and attributed to the formation of voids on the jet surface at the early stage of electrospinning and subsequent elongation and solidification of the voids into a line surface structure. The fast evaporation of a highly volatile solvent, acetone, from the polymer solution was found to play a key role in the formation of surface voids, while the high viscosity of the residual solution after the solvent evaporation ensured the line surface to be maintained after the solidification. Based on this principle, nanofibres having a similar surface texture were also electrospun successfully from other polymers, such as cellulose acetate, polyvinylidene fluoride, poly(methyl methacrylate), polystyrene and poly(vinylidene fluoride-co-hexafluoropropene), either from the same or from different solvent systems. Polarized Fourier transform infrared spectroscopy was used to measure the polymer molecular orientation within nanofibres. Schwann cells were grown on both aligned and randomly oriented nanofibre mats. The parallel line surface texture assisted in the growth of Schwann cells especially at the early stage of cell culture regardless of the fibre orientation. In contrast, the molecular orientation within nanofibres showed little impact on the cell growth.