Collagen is a suitable material for regenerative medicine because it is characterized by its good biocompatibility. However, due to its fibrillar structure, it cannot organize itself into three-dimensional porous structures without additional modification. The introduction of synthetic monomer elements into the collagen macromolecules is a technique used to form three-dimensional, collagen-based, branched, and crosslinked structures. New types of graft copolymers made from cod collagen with a butyl acrylate and vinyl butyl ether copolymer in aqueous dispersion were obtained in the presence of triethylborane by a radical mechanism. The process of graft copolymer formation proceeded as usual by radical initiation, through radicals formed during triethylborane oxidation by oxygen residues, collagen borination, and reversible inhibition with the participation of a boroxyl radical. The characteristics of the graft copolymers were determined using methods of physical and chemical analysis (GPC, SEM, IR spectroscopy, etc.), while the cytotoxicity was assessed using the MTT assay method. It is shown that the grafting of alternating blocks of butyl acrylate and vinyl butyl ether to the protein macromolecules results in changes in the morphological pattern of the graft co-polymer in comparison with native collagen. This is manifested in the development of consolidations around the collagen fibers of the structural matrices, with the co-polymer cellular structure consisting of interpenetrating pores of unequal size. Additionally, it is important that the graft co-polymer solutions are not toxic at a certain concentration. The above properties confirm the promising nature of the technique’s application as the basis for producing new materials for regenerative medicine.