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The catalytic upgrading of bio-based platform molecules is a promising approach for biomass valorization. However, most solid catalysts are not thermally or chemically stable, and are difficult to prepare. In this study, a stable organic phosphonate–hafnium solid catalyst (PPOA–Hf) was synthesized, and acid–base bifunctional sites were found to play a cooperative role in the cascade transfer hydrogenation and cyclization of ethyl levulinate (EL) to γ-valerolactone (GVL). Under relatively mild reaction conditions of 160 °C for 6 h, EL was completely converted to GVL with a good yield of 85%. The apparent activation energy was calculated to be 53 kJ/mol, which was lower than other solid catalysts for the same reaction. In addition, the PPOA-Hf solid catalyst did not significantly decrease its activity after five recycles, and no evident leaching of Hf was observed, indicating its high stability and potential practical application.