In recent years, antibacterial nanosystems with loading and delivery capacity for anticancer agents have received increasingly widespread attention in the field of cancer treatment involving bacterial infection. Silver nanoparticles (AgNPs) are the most representative and widely used biocompatible metallic nanoparticles, which possess long-lasting and broad-spectrum antibacterial activity. However, conventional AgNPs are difficult to load and deliver anticancer agents directly because of their relatively inert surfaces. Herein, biocompatible silver nanoparticles (TA-AgNPs) were prepared via a simple approach in which tannic acid (TA) served as a “green” reducing and stabilizing agent. The resultant TA-AgNPs have low cytotoxicity against normal cells and exhibit significant antibacterial activity. The minimum inhibitory concentration (MIC) value of TA-AgNPs toward Escherichia coli was about 16 μg/mL, and the elimination rate of TA-AgNPs at a concentration of 0.5 mg/mL was above 99 and 93% at 6 h for E. coli and Staphylococcus aureus, respectively. TA-AgNPs have a good ability to load and deliver anticancer drug epirubicin hydrochloride (EPI). EPI can be adsorbed onto the surface of TA-AgNPs by strong electrostatic interaction between TA and EPI. The TA-AgNPs/EPI nanodrug displays a pH- and glutathione (GSH)-sensitive drug release performance through the protonation of phenolic hydroxyl groups in TA under an acid condition and the disassociation of TA molecules from the surface of AgNPs due to the ligand exchange reaction between GSH thiols and TA molecules. The 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay results showed an equal cytotoxicity effect against Hep G2 cells between free EPI and EPI-loaded TA-AgNPs. More importantly, the 3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2H-tetrazolium (MTS) assay results indicated that the cytotoxicity of free EPI was significantly reduced in the presence of bacteria, but the resultant EPI-loaded TA-AgNPs could effectively prevent the influence of bacteria on the cytotoxicity of EPI. The animal tumor suppression and anti-infection model assay results indicated good tumor suppression and antibacterial properties of the TA-AgNPs/EPI nanodrug.