Biodiesel synthesis was carried out via heterogeneous catalysis of canola oil with nanoparticles of a mixed oxide based on rare earths. The catalyst synthesis (NdAlO3) was carried out based on the method proposed by Pechini for the synthesis of nanoparticles. Thermogravimetric analysis-differential thermal analysis (TGA-DTA) analysis was performed on the nanoparticle precursor gel in order to establish the optimum conditions for its calcination, with these being of 800 °C over 24 h. A pure NdAlO3 compound with an approximate size of 100 nm was obtained. The products of the transesterification reaction were analyzed using gas chromatography, FTIR, and NMR. The optimum reaction conditions were determined, namely, the temperature effect, reaction time, methanol:oil mass ratio, and recyclability of the catalyst. These studies showed the following optimal conditions: 200 °C, 5 h, methanol:oil mass ratio of 6:1, and a constant decrease in the catalytic activity of the catalyst was observed for up to six reuses, which later remained constant at around a 50% conversion rate. The maximum biodiesel yield obtained with the optimum conditions was around 75%. Analysis of the reaction products showed that the residual oil showed a chemical composition different from that of the source oil, and that both the biodiesel and glycerol obtained were of high purity.