The present invention provides a process for the enzymatic degumming of unrefined triglyceride oils, said process comprising: a) providing an unrefined triglyceride oil having a phosphorus content of at least 100 mg per kg of unrefined triglyceride oil; b) combining the unrefined triglyceride oil with water, lactic acid and enzyme to produce an oil-and-water emulsion, said enzyme being selected from phospholipase, lipid acyltransferase and combinations thereof; c) keeping the emulsion at temperature of 20-90°C for at least 10 minutes; and d) separating degummed triglyceride oil from the emulsion. This enzymatic degumming process is extremely effective in removing phospholipids, including non-hydratable phospholipids (NHP), from crude and other unrefined vegetable oils.