This study presents the fabrication of a glucose biosensor based on the immobilization of glucose oxidase (GOx) on Pd nanoparticles (PdNPs) loaded (3-aminopropyl)triethoxysilane (APTES) functionalized reduced graphene oxide (rGO-APTES) and non-enzymatic H2O2 sensor based on Pd@rGO-APTES nanocomposite modified glassy carbon electrode (GCE). Also, Nafion (Nf) was used as a protective membrane for the sensor and biosensor. The electrocatalytic properties of the sensor and biosensor were investigated using electrochemical impedance spectroscopy, cyclic voltammetry, and amperometry. The Nf/Pd@rGO-APTES/GOx/GCE biosensor sensitively measured glucose and showed a linear range from 3 mu M to 4.57 mM with a detection limit (LOD) of 0.91 mu M. The biosensor had a sensitivity of 234.1 mu A mM(-1) cm(-2) and an acceptable selectivity for glucose. The Nf/Pd@rGO-APTES/GCE nanocomposites had an excellent electrochemical response to the reduction of H2O2. The linear range of the sensor for the detection of H2O2 concentration was from 0.7 mu M to 13.5 mM with 0.21 mu M of LOD. The sensitivity was calculated to be 1164.3 mu A mM(-1) cm(-2). In addition, the sensor and biosensor showed excellent sensitivity, selectivity, response time, linear range, LOD, repeatability, reproducibility, and storage stability when compared with reported sensors and biosensors.