The invention discloses a naphthoxazine-based polymer and a naphthoxazine-based porous carbon fiber and preparation methods thereof, belonging to the technical field of carbon fibers. According to the invention, naphthoxazine containing an alcoholic hydroxyl group reacts with an acyl chloride reagent under certain conditions so as to prepare naphthoxazine-based acrylate, and then under the action of an initiator, naphthoxazine-based acrylate undergoes polymerization so as to obtain the naphthoxazine-based polymer; the polymer, a pore forming agent and a solvent are mixed, and static spinning is carried out so as to prepare naphthoxazine-based protofilament; and the protofilament is subjected to curing at a constant temperature of 160 to 250 DEG C for 2 to 5 h, then to carbonization at a constant temperature of 600 to 1200 DEG C for 60 to 200 min and finally cooled to room temperature so as to obtain the naphthoxazine-based porous carbon fiber. The carbon fiber prepared in the invention has the advantages of a high carbon yield ratio, low shrinkage, simple carbonization, a hierarchical pore structure and uniform particle size distribution and can be used in the field of energy storage electrode materials.