Graphene has attracted much attention in biosensing applications due to its unique properties. In this paper, the monolayer graphene was grown by chemical vapor deposition (CVD) method. Using the graphene as the electric channel, we have fabricated a graphene field-effect transistor (G-FET) biosensor that can be used for label-free detection of RNA. Compared with conventional method, the G-FET RNA biosensor can be run in low cost, be time-saving, and be miniaturized for RNA measurement. The sensors show high performance and achieve the RNA detection sensitivity as low as 0.1 fM, which is two orders of magnitude lower than the previously reports. Moreover, the G-FET biosensor can readily distinguish target RNA from noncomplementary RNA, showing high selectivity for RNA detection. The developed G-FET RNA biosensor with high sensitivity, fast analysis speed, and simple operation may provide a new feasible direction for RNA research and biosensing.