In this work, a facile, environmentally friendly method was demonstrated for the synthesis of Ag-Au bimetallic nanoparticles (Ag-AuNPs) supported on reduced graphene oxide (RGO) with alginate as reductant and stabilizer. The prepared Ag-AuNPs/RGO was characterized by scanning electron microscope (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). The results indicated that uniform, spherical Ag-AuNPs was evenly dispersed on graphene surface and the average particle size is about 15 nm. Further, a non-enzymatic sensor was subsequently constructed through the modified electrode with the synthesized Ag-AuNPs/RGO. The sensor showed excellent performance toward H2O2 with a sensitivity of 112.05 μA·cm−2·mM−1, a linear range of 0.1–10 mM, and a low detection limit of 0.57 μM (S/N = 3). Additionally, the sensor displayed high sensitivity, selectivity, and stability for the detection of H2O2. The results demonstrated that Ag-AuNPs/RGO has potential applications as sensing material for quantitative determination of H2O2.