In recent years, the coupling of structurally and functionally controllable polymers with biologically active protein materials to obtain polymer-protein conjugates with excellent overall properties and good biocompatibility has been important research in the field of polymers. In this study, the hyperbranched polymer hP(DEGMA-co-OEGMA) was first prepared by combining self-condensation vinyl polymerization (SCVP) with photo-induced metal-free atom transfer radical polymerization (ATRP), with 2-(2-bromo-2-methylpropanoyloxy) ethyl methacrylate (BMA) as inimer, and Di (ethylene glycol) methyl ether methacrylate (DEGMA) and (oligoethylene glycol) methacrylate (OEGMA, Mn = 300) as the copolymer monomer. Then, hP(DEGMA-co-OEGMA) was used as a macroinitiator to continue the polymerization of a segment of pyridyl disulfide ethyl methacrylate (DSMA) monomer to obtain the hyperbranched multiarm copolymers hP(DEGMA-co-OEGMA)-star-PDSMA. Finally, the lysozyme with sulfhydryl groups was affixed to the hyperbranched multiarm copolymers by the exchange reaction between sulfhydryl groups and disulfide bonds to obtain the copolymer protein conjugates hP(DEGMA-co-OEGMA)-star-PLZ. Three hyperbranched multiarm copolymers with relatively close molecular weights but different degrees of branching were prepared, and all three conjugates could self-assemble to form nanoscale vesicle assemblies with narrow dispersion. The biological activity and secondary structure of lysozyme on the assemblies remained essentially unchanged.