We present an aptameric graphene field-effect transistor (GFET) nanosensor for sensitive and label-free detection of biomarkers in serum. The graphene nanosensor is serially functionalized with a polyethylene glycol (PEG) nanolayer and an aptamer for specific detection of a target analyte and effective rejection of background molecules in human serum. The analyte binds to the surface-immobilized aptamer, changing the carrier concentration in the graphene. The resulting changes in the conductance of the graphene is measured to determine the analyte concentration. Experimental results show that the device is capable of detecting immunoglobulin E (IgE) in serum in a clinically relevant range of 50 pM to 35 nM.