Graphene quantum dots (GQDs) are becoming an efficient nanomaterial to control their optoelectronic properties by molecular engineering due to the advantages of tunability by size, shape, doping, and comparatively low degree of toxicity and a great extent of spatial confinement. Their bandgap can be tuned effectively by functionalization of their surface or edges with some specific groups. In the present study, systematic efforts have been made to tune the band gap and corresponding optical properties of the GQDs by functionalizing them with different aryl amine groups because of their potential for extremely strong and wide-ranging light absorption; these GQDs have also been demonstrated to be advantageous for photocatalysis. The absorption and fluorescence spectra have been investigated by employing density functional theory with Becke three parameters hybrid functional with Lee-Yang-Perdew (B3LYP) correlation functional as implemented in Gaussian 09 package. Functionalization with such aryl amine groups accounts for the decrement in band gap and shift of absorption spectra towards longer wavelength. Such narrow band gap GQDs are highly required for the applications such as photocatalysis and bio-imaging etc. The outcomes achieved in this way are highly consistent with other experimental findings.