The invention relates to a method for preparing biodegradable solid-solid phase transition nano fibers or fiber membranes, which comprises: (1) adding a coupling agent and a catalyst into water dispersion of cellulose nanocrystals in turn, dripping dehydrant-containing ethanol solution, stirring, reacting for 6 to 10 hours to prepare water dispersion of carboxyl cellulose nanocrystals; (2) adding PEG and a catalyst into the water dispersion of carboxyl cellulose nanocrystals in turn, dripping the dehydrant-containing ethanol solution, stirring and reacting for 10 to 12 hours to obtain polyethylene glycol grafted cellulose nanocrystal graft copolymer; and (3) preparing aqueous solution of the graft copolymer as spinning solution and spinning. In the invention, the cost is low, the whole preparation process is performed in a water system, the preparation process is simple, easy to control and suitable for industrial production; and the obtained biodegradable solid-solid phase transition nano fibers or fiber membranes have the advantages of high storage capacity and proper phase transition temperature and the like.