Nanomaterial-based field-effect transistor (FET) sensors are capable of label-free real-time chemical and biological detection with high sensitivity and spatial resolution, although direct measurements in high-ionic-strength physiological solutions remain challenging due to the Debye screening effect. Recently, we demonstrated a general strategy to overcome this challenge by incorporating a biomolecule-permeable polymer layer on the surface of silicon nanowire FET sensors. The permeable polymer layer can increase the effective screening length immediately adjacent to the device surface and thereby enable real-time detection of biomolecules in high-ionic-strength solutions. Here, we describe studies demonstrating both the generality of this concept and application to specific protein detection using graphene FET sensors. Concentration-dependent measurements made with polyethylene glycol (PEG)-modified graphene devices exhibited real-time reversible detection of prostate specific antigen (PSA) from 1 to 1,000 nM in 100 mM phosphate buffer. In addition, comodification of graphene devices with PEG and DNA aptamers yielded specific irreversible binding and detection of PSA in pH 7.4 1x PBS solutions, whereas control experiments with proteins that do not bind to the aptamer showed smaller reversible signals. In addition, the active aptamer receptor of the modified graphene devices could be regenerated to yield multiuse selective PSA sensing under physiological conditions. The current work presents an important concept toward the application of nanomaterial-based FET sensors for biochemical sensing in physiological environments and thus could lead to powerful tools for basic research and healthcare.