Bacterial infection and osteogenic integration are the two main problems that cause severe complications after surgeries. In this study, the antibacterial and osteogenic properties were simultaneously introduced in biomaterials, where copper nanoparticles (CuNPs) were generated by in situ reductions of Cu ions into a mussel-inspired hyperbranched polyglycerol (MI-hPG) coating via a simple dip-coating method. This hyperbranched polyglycerol with 10 % catechol groups’ modification presents excellent antifouling property, which could effectively reduce bacteria adhesion on the surface. In this work, polycaprolactone (PCL) electrospun fiber membrane was selected as the substrate, which is commonly used in biomedical implants in bone regeneration and cardiovascular stents because of its good biocompatibility and easy post-modification. The as-fabricated CuNPs-incorporated PCL membrane [PCL-(MI-hPG)-CuNPs] was confirmed with effective antibacterial performance via in vitro antibacterial tests against Staphylococcus aureus (S. aureus), Escherichia coli (E. coli), and multi-resistant E. coli. In addition, the in vitro results demonstrated that osteogenic property of PCL-(MI-hPG)-CuNPs was realized by upregulating the osteoblast-related gene expressions and protein activity. This study shows that antibacterial and osteogenic properties can be balanced in a surface coating by introducing CuNPs.