Förster resonance energy transfer (FRET), referred to as the transfer of the photon energy absorbed in donor to acceptor, has received much attention as an important physical phenomenon for its potential applications in optoelectronic devices as well as for the understanding of some biological systems. If one-atom-thick graphene is used for donor or acceptor, it can minimize the separation between donor and acceptor, thereby maximizing the FRET efficiency (EFRET). Here, we report first fabrication of a FRET system composed of silica nanoparticles (SNPs) and graphene quantum dots (GQDs) as donors and acceptors, respectively. The FRET from SNPs to GQDs with an EFRET of ∼78% is demonstrated from excitation-dependent photoluminescence spectra and decay curves. The photodetector (PD) responsivity (R) of the FRET system at 532 nm is enhanced by 100∼101/102∼103 times under forward/reverse biases, respectively, compared to the PD containing solely GQDs. This remarkable enhancement is understood by network-like current paths formed by the GQDs on the SNPs and easy transfer of the carriers generated from the SNPs into the GQDs due to their close attachment. The R is 2∼3 times further enhanced at 325 nm by the FRET effect.