Hollow gold-silver bimetallic nanoparticles (AuAg-HNPs) have been synthesized and their optical and structural properties were characterized. Initially Ag nanoparticles (Ag-NPs) were prepared using poly(ethylenimine) (PEI) as a reducing and a stabilizing agent simultaneously. AuAg-HNPs could then be synthesized via galvanic replacement reaction in a PEI aqueous solution by reacting sacrificial Ag template with a precursor compound of Au, i.e., $HAuCl_4$. Due to the presence of abundant amine functional groups in PEI, which could act as the dissolving ligand for AgCl, the precipitation problem of $Ag^+$ in the presence of Cl from $HAuCl_4$ salt was avoided. On this basis, the relatively high concentrations of $HAuCl_4$ and PEI-stabilized Ag nanoparticles could be used for the fabrication of AuAg-HNPs. Because of their increased surface areas and reduced densities, the AuAg-HNPs were expected and confirmed to outperform their solid counterparts in applications such as catalysis for the reduction of 4-nitrophenol in the presence of $NaBH_4$.