In this study, a new graft copolymer, P(AN-co-AM)-g-MAPEG, was synthesized by polyethylene glycol monoester of maleic acid (MAPEG), acrylonitrile (AN), and a third monomer acrylamide (AM) in water phase precipitation, in which random copolymer of P(AN-co-AM) was taken as skeleton and macromonomer MAPEG with phase transition as branched chain. The P(AN-co-AM)-g-MAPEG nanofibers were prepared by electrostatic spinning. The effects of pinhole diameter, spinning solution concentration, and spinning liquid solvent on the structure of nanofibers were investigated by scanning electron microscopy. The structure, phase-change properties, and thermal stability of the grafted copolymer were characterized by Fourier transform infrared spectroscopy, differential scanning calorimetry, and X-ray diffraction. The results show that the new solid-solid phase-change material P(AN-co-AM)-g-MAPEG was successfully prepared. The nanofiber diameter increased with the increasing pinhole diameter. The obtained phase-change nanofibers exhibit good phase transition and thermal stability.