A novel heterogeneous bi-functional catalyst namely silicon carbide/sodium hydroxide-graphene oxide (SiC/NaOH-GO) was successfully developed and characterized using fourier transform infrared spectroscopy (FT-IR), thermogravimetry analysis (TGA), scanning electron microscope (SEM), energy disperse X-ray analysis (EDX), Brunauer Emmett Teller analysis (BET), X-ray diffraction (XRD), carbon dioxide temperature programmed desorption of carbon dioxide (CO2-TPD) and ammonia temperature programmed-desorption (NH3-TPD). The catalyst was applied in microwave-assisted transesterification and esterification of binary model feedstock (rapeseed oil and oleic acid) containing 20% free fatty acid (FFA) and optimized using respond surface methodology (RSM) based on centre composite design. The study revealed that the optimum reaction conditions were 13:1 wt ratio of SiC/NaOH to GO, 5 wt% of catalyst loading, reaction temperature of 65 degrees C and 6 min reaction time to attain 96% of yield of transesterification and 92% of yield of esterification. Then, the optimized catalyst (13:1 wt ratio of SiC/NaOH) was applied in Chlorella vulgaris lipid with high free fatty acid content (26%) to further confirmed the ability of converting triglycerides and free fatty acid (FFA) to biodiesel simultaneously. The study revealed that 92% of FFA of microalgae lipid was converted and 81% of fatty acid methyl ester content (FAME) was attained under the optimum conditions of methanol to lipid molar ratio of 48, 5 min reaction time, 4 wt% catalyst and reaction temperature of 85 degrees C.