Developing an efficient one-pot catalytic process for biodiesel production from non-edible oils under mild reaction conditions remains challenging. Here, a novel process for the one-pot conversion of non-edible Firmiana platanifolio L.f. (FPLF) oil into biodiesel using inexpensive, scalable imidazolium salts-based solid acid containing both Bronsted and Lewis acid sites as the catalyst was investigated for the first time. The Bronsted-Lewis acid bifunctional catalyst ([DSI][FeCl4]) was synthesized facilely and atom-economically (the final product contains the high amounts of atoms from the reactants) from 1,3-disulfonic acid imidazolium chloride ([DSI][Cl]) with FeCl3 and was characterized by FT-IR, H-1 and C-13 NMR, N-2 adsorption-desorption, SEM-EDS, TEM, FT-IR of pyridine, NH3 -TPD, TGA and elemental analysis. Owing to the presence of immiscible phases of oil and methanol in the reaction mixture, the effects of various co-solvents on the conversion of the FPLF oil into biodiesel were investigated, with the aim of reducing the mass transfer resistance. The results demonstrated that biomass-derived tetrahydrofuran (THF) was a superior co-solvent and could improve the reaction rate and biodiesel yield. The reaction conditions were optimized by using response surface methodology (RSM), [DSI][FeCl4] exhibited excellent catalytic performance, with a high biodiesel yield of 98.7% under the following mild reaction conditions, which was superior to that of commercial resins (e.g., Amberlyst 15 and Nafion NR50). Detailed kinetic studies demonstrated that the catalytic process followed first-order kinetics and that the activation energy (83.56 kJ/mol) was relatively low compared to previous results. Thermodynamic analysis revealed that the catalytic process was non-spontaneous and that the reaction was endothermic and endergonic. Intriguingly, the catalyst was a heterogeneous catalyst during the reaction and maintained high catalytic activity after four cycles. The fuel properties of biodiesels derived from FPLF oil complied with the corresponding ASTM D6751 and EN14214 standards.