Tolerance nutritional product to supplement human milk

The invention relates to a nutritional supplement for human milk to feed premature infants comprising protein, fat and carbohydrates wherein the carbohydrate content is limited to no more than about 10% dry weight of the nutritional supplement, and the fat content is at least about 35% dry weight, to reduce the increase in osmolality occurring when the supplement is added to human milk and, thus, produce a supplemented human milk that is better tolerated by the infants. Vitamins and minerals can be added. The present invention relates also to methods to support the rapid growth of premature infants by administering nutritionally supplemented human milk to those infants.