We have investigated molecule adsorption phenomena on a chemically active surface of titanium oxide nanosheet by coupling with an electrically sensitive graphene field effect transistor (FET). Super-hydrophilic surface of the titanium oxide nanosheet forms a water-layer in ambient air which exhibits a large hysteresis of drain current in the hybrid FET for sweeping gate-voltage. The large hysteresis disappears in vacuum, which indicates physically adsorbed water molecules on the surface of the titanium oxide nanosheet dominantly contribute to the hysteresis. UV light irradiation in vacuum significantly changes the drain current due to desorption of the adsorbed molecules. Sufficient UV irradiation results in symmetric gate-voltage dependence similar to those of conventional graphene FETs. Exposure to an oxygen gas atmosphere leads to a heavy hole doping in the FET, where the binding of the oxygen molecules is stronger than that of water molecules. In a humidified nitrogen atmosphere, a large shift of charge neutrality point is observed in transfer characteristics crossing between electron doping and hole doping. By contrast, a clear square-shaped hysteresis loop is observed in a humidified oxygen atmosphere, where the hole density in the graphene drastically changed with O2/H2O redox couple reaction on the titanium oxide nanosheet.