The invention discloses a photo-crosslinking stabilized hyperbranched free radical polymer and a preparation method and application thereof. 2,2,6,6-tetramethyl-4-piperidyl methacrylate, a photo-crosslinked monomer and a branched monomer are subjected to free radical polymerization and then an oxidation reaction, and the hyperbranched free radical polymer is obtained. The polymer has a structure unit which can be ultraviolet photo crosslinked, after the structure is compounded with carbon materials, stabilization of in situ photo crosslinking can be achieved, the situation that the polymer isdissolved out in electrolyte, the service life is thus shortened and repeated charging is not allowed, the cycling stability of a battery is improved, no additional crosslinking agent or binder needsto be added, the adverse effects of adding materials on an electrode are avoided, moreover, the polymer has the hyperbranched structure which can be crosslinked, the dispersing performance is good, meanwhile the molecular weight and the glass transition temperature are significantly improved, the mechanical properties are good, and the application prospect is wide.