The invention relates to a nutritional supplement for human milk in powder or liquid form to feed premature infants comprising protein, fat and carbohydrates wherein the carbohydrate content is limited to no more than 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.