The article presents the results of research on the synthesis of a new biopolyol based on evening primrose oil, and its use in the production of rigid polyurethane–polyisocyanurate foams intended for thermal insulation. The obtained biopolyol was subjected to analytical, physicochemical, and spectroscopic tests (Fourier transform infrared (FTIR), 1H NMR, 13C NMR) to confirm its suitability for the synthesis of polyurethane materials. Then, it was used for the partial replacement of the petrochemical polyol in the polyurethane formulation. Obtained rigid polyurethane–polyisocyanurate foams are characterized by a lower apparent density, brittleness, water absorption, and thermal conductivity coefficient λ. In addition, foams modified by biopolyols had a higher content of closed cells and higher aging resistance. The results of the conducted research showed that the use of the biopolyol based on evening primrose oil may be an alternative to petrochemical polyols. The research presented herein is perfectly consistent with the trends of sustainable development and the philosophy of green chemistry.