Generally, the anchoring of inorganic nanoparticles onto the surface of fibers faces the problem of poor stability, which limits the wide application of nanoparticle functionalized fibers. Herein, nanofibers with shell-core structures were constructed by coaxial electrospinning of two polymers with different melting points (Tm). Polyglycolic acid (PGA, Tm = 225 °C) was employed as the core layer, while polycaprolactone (PCL, Tm = 60 °C) was used as the shell layer. Silver nanoparticles (AgNPs) were electrosprayed on the nanofibers and the shell layer (PCL) was heated and melted to bond the AgNPs, thus realizing a stable AgNP-composited nanofiber for the construction of antibacterial functional surface. By regulating the shell-core flow ratio and the condition for heat treatment, the appropriate thickness of the shell layer was obtained with a flow ratio of 3:1 (PCL:PGA). The optimal composite structure was constructed when the thermal bonding was taken under 80 °C for 5 min. Furthermore, it was found that the composite nanofibers prepared by thermal bonding had better hydrophilicity, mechanical property, and AgNPs bonding stability, and their antibacterial rate against Staphylococcus aureus (S. aureus) reached over 97%. Overall, a facile and universal method for the preparation of nanoparticle-anchored nanofibers was established in this study. The robust nanoparticle-composited nanofibers are promising for applications in optoelectronic devices, electrode materials, and so on.