This work focuses on the study of biodiesel production from commercial rapeseed oil and methanol via transesterification reactions on monometallic copper and bimetallic copper–noble metal (platinum, ruthenium) catalysts supported on BEA zeolite. The catalysts were prepared by wet impregnation method on the hydrogen form of BEA zeolite. As part of the study, the physicochemical and catalytic properties of the prepared catalytic materials were determined. The catalytic activity tests were carried out in the transesterification reaction over prepared catalysts at 220 °C for 2 h in an autoclave. The physicochemical properties of the obtained catalysts were investigated by X-ray diffraction (XRD), specific surface area and porosity (BET), a scanning electron microscope equipped with an energy dispersive spectrometer (SEM–EDS) and temperature-programmed desorption of ammonia (TPD-NH3) method. The results of the catalytic activity showed the promotional effect of the noble metal on the TG conversion and FAME efficiency of copper catalysts in the biodiesel production process. The most active catalyst turned out to be the calcined 5%Cu–1%Ru/BEA catalyst, which showed the highest TG conversion of 85.7% and the second highest FAME efficiency of 58.4%. The high activity of this system is explained by its surface acidity and large specific surface area.