Triglyceride oil derived from marine sources, mammalian and fish, is treated with a silica at relatively low temperature under vacuum and is then further treated with a bleaching clay under vacuum and at higher temperature. The silica and the bleaching clay are then separated from the oil. The oil treated by this method is essentially free of proteinaceous materials, phosphatides and mucilage, pro-oxidant metals and very low in colored compounds, and is suitable for deodorizing. The deodorized oil is completely bland, unchanged in the concentration of the long-chain highly unsaturated fatty acids (EPA, DPA and DHA), very low in color, peroxides and secondary oxidation products, free of pesticides and has very good flavor stability. The method avoids the use of any chemicals, such as in the acid and base treatments required in conventional degumming and alkali refining of oils of marine origin. This avoids the formation of artifacts in the oil and trace contamination with chemicals. It also reduces the number of process steps required to produce deodorized food oil from marine sources, which is advantageous in respect to oil quality, process losses and processing costs. The method is especially environmentally advantageous, since it avoids the need for soapstock and waste water processing entirely. Refined oil produced by the method is useful as a nutritional supplement and in methods of therapy or medical treatment.