Graphene field-effect transistors (GFETs) were fabricated by photolithography and lift-off processes, and subsequently heated in a rapid-thermal-annealing (RTA) apparatus at temperatures (T(A)) from 200 to 400 °C for 10 min under nitrogen to eliminate the residues adsorbed on the graphene during the GFET fabrication processes. Raman-scattering, current-voltage (I-V), and sheet resistance measurements showed that, after annealing at 250 °C, graphene in GFETs regained its intrinsic properties, such as very small intensity ratios of D to G and G to 2D Raman bands, a symmetric I-V curve with respect to ~0 V, and very low sheet resistance. Atomic force microscopy images and height profiles also showed that the surface roughness of graphene was almost minimized at T(A) = 250 °C. By annealing at 250 °C, the electron and hole mobilities reached their maxima of 4587 and 4605 cm(2) V(-1) s(-1), respectively, the highest ever reported for chemical-vapor-deposition-grown graphene. Annealing was also performed under vacuum or hydrogen, but this was not so effective as under nitrogen. These results suggest that the RTA technique is very useful for eliminating the surface residues of graphene in GFETs, in that it employs a relatively low thermal budget of 250 °C and 10 min.