Methotrexate (MTX), a widely used anticancer drug, is a refractory organic pollutant posing serious threats to ecosystems and human health. This study focuses on the development of a novel catalyst composed of Ce-based high-entropy metal oxides (NHEMO) supported on nepheline for the catalytic wet peroxide oxidation (CWPO) process, targeting MTX degradation in simulated wastewater. The NHEMO catalyst exhibited a unique high-entropy structure that enhances catalytic performance by facilitating diverse electronic interactions, which was confirmed through X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses showing a well-defined crystal structure and uniform dispersion of metal oxides. Additionally, X-ray photoelectron spectroscopy (XPS) and energy-dispersive X-ray spectroscopy (EDS) revealed a stable metal composition and high oxidation states of active metal sites. At a reaction temperature of 160 °C, with a residence time of 150 s and an oxidation coefficient of 5, the catalyst achieved a MTX removal rate of 93.49 % and a chemical oxygen demand (COD) removal of 99.95 %. Density Functional Theory (DFT) calculations further demonstrated that H2O2 decomposes into both adsorbed (surface-bound) and free (solution-phase) hydroxyl radicals (·OH). These radicals synergistically degrade MTX through both radical and non-radical pathways, ensuring comprehensive pollutant breakdown. The catalyst also showed excellent stability and a very low metal dissolution rate during the reaction, maintaining high catalytic activity after repeated recycling. This catalyst offers high cost-effectiveness, activity, and stability, providing a promising solution for treating refractory organic pollutants in pharmaceutical wastewater.