Cu/Sn/C composite nanofibers were synthesized by using dual-nozzle electrospinning and subsequent carbonization. The composite nanofibers are a homogeneous amorphous matrix comprised of Cu, Sn, and C with a trace of crystalline Sn. The Li- and Na-ion storage performance of the Cu/Sn/C fiber electrodes were investigated by using cyclic voltammetry, galvanostatic cycling, and electrochemical impedance spectroscopy. Excellent, stable cycling performance indicates capacities of 490 and 220 mAhg(-1) for Li-ion (600 cycles) and Na-ion (200 cycles) batteries, respectively. This is a significant improvement over other reported Sn/C nanocomposite devices. These superior electrochemical properties could be attributed to the advantages of incorporating one-dimensional nanostructures into the electrodes, such as short electron diffusion lengths, large specific surface areas, ideal homogeneous structures for buffering volume changes, and better electronic conductivity that results from the amorphous copper and carbon matrix.