The excessive use of traditional antibiotic and antibacterial agents has globally increased the growth of antibiotic-resistant bacteria that poses serious health risks. Therefore, the development of new generation antibacterial or antimicrobial agents for effective inhibition of bacterial growth is highly desired. In this study, we report a facile one-step synthesis approach for the preparation of a nanocomposite composed of silver nanoparticles (AgNPs) decorated with sulfur-doped graphene quantum dots (S-GQDs). The nanocomposite was comprehensively characterized using transmission electron microscopy (TEM), X-ray diffraction (XRD), UV-vis absorption spectra, Fourier transform infrared (FTIR) spectroscopy and X-ray photoelectron spectroscopy (XPS). The characterization results demonstrated that the AgNPs were closely and uniformly surrounded by the S-GQDs, and consequently, this ensured the dispersion and stability of the so formed nanocomposite (Ag@S-GQDs). Further, the antibacterial activity of the Ag@S-GQDs nanocomposite was investigated and compared with bare S-GQDs and AgNPs against Gram-positive S. aureus (MTCC 737) and Gram-negative P. aeruginosa (MTCC 424) bacteria using macrodilution and agar well diffusion methods. Minimum inhibitory concentration (MIC) values of 70 and 35 μg mL-1 of the Ag@S-GQDs nanocomposite were found to be sufficient to hinder the growth of P. aeruginosa and S. aureus. A fractional inhibition concentration (FIC) index below 0.5 confirmed the existence of a synergistic effect between AgNPs and S-GQDs in the Ag@S-GQDs nanocomposite. In addition, the cytotoxicity of the Ag@S-GQDs nanocomposite, AgNPs and S-GQDs was also investigated using HEK 293 cell lines. Interestingly, the Ag@S-GQDs nanocomposite exhibited superior cell viability as compared to AgNPs and S-GQDs. These improved antibacterial and biocompatibility data demonstrate that the Ag@S-GQDs nanocomposite can serve as a promising antibacterial agent for industry to fabricate next-generation self-sterile textiles, antibacterial coatings and useful health care products supporting cell viability.