A green facile method has been successfully used for the synthesis of graphene oxide sheets decorated with silver nanoparticles (rGO/AgNPs), employing graphite oxide as a precursor of graphene oxide (GO), AgNO3 as a precursor of Ag nanoparticles (AgNPs), and geranium (Pelargonium graveolens) extract as reducing agent. Synthesis was accomplished using the weight ratios 1:1 and 1:3 GO/Ag, respectively. The synthesised nanocomposites were characterised by scanning electron microscopy, transmission electron microscopy, atomic force microscopy, X-ray diffraction, UV-visible spectroscopy, Raman spectroscopy, energy dispersive X-ray spectroscopy and thermogravimetric analysis. The results show a more uniform and homogeneous distribution of AgNPs on the surface of the GO sheets with the weight ratio 1:1 in comparison with the ratio 1:3. This eco-friendly method provides a rGO/AgNPs nanocomposite with promising applications, such as surface enhanced Raman scattering, catalysis, biomedical material and antibacterial agent.