In this study, polyols with high average functionality were synthesized from a renewable resource, rapeseed oil, as raw material for rigid PU foam production. A well-known method of rapeseed oil fatty acid double bond epoxidation was used to introduce oxirane rings into rapeseed oil structure. The temperature influence on epoxidation reaction conversion rate was studied by volumetric and FTIR spectra analysis. After epoxidation of rapeseed oil, an oxirane ring-opening reaction was carried out to obtain high functionality polyols. Diethylene glycol, a conventional oxirane ring-opening reagent, was compared to amine-based polyfunctional alcohols, diethanolamine and triethanolamine. The introduction of tertiary amine groups into the polyol structure provided catalytical properties for obtained polyols, which will allow a reduction of the amount of catalysts in polyurethane foam formulations. Hydroxyl value, acid value, moisture content, viscosity and density of synthesized polyols were determined, and their structure and average functionality were analyzed by FTIR and MALDI-TOF spectroscopy and GPC analysis. Also, the main characteristics of rigid PU foam obtained from synthesized polyols were determined.