The nonlinear optical properties of silver-nanoparticle-decorated functionalized (hydrogen-induced reduction, exfoliated) multilayered graphene (AgNP/fG) composite have been investigated in the picosecond time scale by using the Z-scan technique. Drastic changes in the Z-scan profiles are obtained in AgNP/fG at 1064 nm as the profile flips from the behavior of strong saturable absorption (SA) to reverse saturable absorption (RSA) on increasing the incident intensity. On the other hand, in graphene, the effect of weaker SA is observed at low intensities, but it flips to RSA at higher incident intensities. The strong SA in the case of the composite has been attributed to the electronic interaction between graphene and silver nanoparticles. The metallic plasmonic transition has a contribution to the optical nonlinearity in AgNP/fG at 532 nm. © 2012 Optical Society of America.