We explore the mechanism of the fluorescence enhancement and fluorescence quenching effect of single walled carbon nanotubes (SWCNTs) on highly fluorescent graphene quantum dots (GQDs) over a wide range of concentrations of SWCNTs. At very low concentrations of SWCNTs, the fluorescence intensity of the GQDs is enhanced, while at higher concentrations, systematic quenching of fluorescence is observed. The nature of the Stern-Volmer plot for the latter case was found to be non-linear indicating a combined effect of dynamic and static quenching. The contribution of the dynamic quenching component was assessed through the fluorescence lifetime measurements. The contribution of static quenching is confirmed from the red shift of the fluorescence spectra of the GQDs after addition of SWCNTs. The fluorescence intensity is first enhanced at very low concentration due to improved dispersion and higher absorption by GQDs, while at higher concentration, the fluorescence of GQDs is quenched due to the complex formation and associated reduction of the radiative sites of the GQDs, which is confirmed from time-resolved fluorescence measurements. Laser confocal microscopy imaging provides direct evidence of the enhancement and quenching of fluorescence at low and high concentrations of SWCNTs, respectively. This study provides an important insight into tuning the fluorescence of GQDs and understanding the interaction between GQDs and different CNTs, which is important for bio-imaging and drug delivery applications.