A fully integrated graphene field-effect transistor (GFET) nanosensor utilizing a novel high-kappa solid-gating geometry for a practical biosensor with enhanced sensitivity is presented. Herein, an "in plane" gate supplying electrical field through a 30 nm HfO2 dielectric layer is employed to eliminate the cumbrous external wire electrode in conventional liquid-gate GFET nanosensors that undesirably limits the device potential in on-site sensing applications. In addition to the advantage in the device integration degree, the transconductance level is found to be increased by about 50% over liquid-gate GFET devices in aqueous-media, thereby improves the sensitivity performance in sensor applications. As the first demonstration of biosensing applications, a small-molecule antibiotic, kanamycin A, is detected by means of an aptameric competitive affinity principle. It is experimentally shown that the label-free and specific quantification of kanamycin A with a concentration resolution at 11.5 x 10(-9) M is achievable through a single direct observation of the 200 s fast bioassay without any further noise canceling. These results demonstrate the utility and practicability of the new devices in label-free biosensing as a novel analytical tool, and potentially hold great promise in other significant biomedical applications.