Levulinic acid is considered one of the most important platform chemicals. It is currently produced mainly from lignocellulosic biomasses. However, there are also other abundant biomass materials, which could be used as raw materials for levulinic acid production. In this work, levulinic acid was produced from two novel biomasses in the presence of Brønsted (H2SO4) and Lewis acid (CrCl3·6H2O or AlCl3·6H2O) catalysts. The studied materials were carbohydrate-rich potato peel waste and sporocarps of the fungus Cortinarius armillatus. Reaction conditions, i.e., time, temperature, H2SO4, and Lewis acid concentrations, were studied by utilizing full 24-factorial experimental designs. Microwave irradiation was used as the heating method. Based on the results, the reaction temperature and the H2SO4 concentration had the greatest impact on the yield of levulinic acid. The highest yield obtained in this study from potato peel waste was 49% with 180 °C for reaction temperature, 15 min for reaction time, and 0.5 and 0.0075 M for the concentrations of H2SO4 and CrCl3, respectively. When Cortinarius armillatus was used as the raw material, the highest yield was 62% with 180 °C for reaction temperature, 40 min for reaction time, and 0.5 and 0.0075 M for the concentrations of H2SO4 and CrCl3, respectively.