Human milk fat has a distinctive stereoisomeric structure where palmitic acid is esterified to the middle (sn-2) position on the glycerol backbone of the triacylglycerol and unsaturated fatty acids to the outer (sn-1/3) positions. This configuration allows for more efficient nutrient absorption in the infant gut. However, the fat used in most infant formulas originates from plants, which exclude palmitic acid from the sn-2 position. Oleaginous yeasts provide an alternative source of lipids for human nutrition. However, these yeasts also exclude palmitic acid from the sn-2 position of their triacylglycerol. Here we show that Yarrowia lipolytica can be engineered to produce triacylglycerol with more than 60% of the palmitic acid in the sn-2 position, by expression of lysophosphatidic acid acyltransferases with palmitoyl-Coenzyme A specificity. The engineered Y. lipolytica strains can be cultured on glycerol, glucose, palm oil or a mixture of substrates, under nitrogen limited condition, to produce triacylglycerol with a fatty acid composition that resembles human milk fat, in terms of the major molecular species (palmitic, oleic and linoleic acids). Culture on palm oil or a mixture of glucose and palm oil produced the highest lipid titre and a triacylglycerol composition that is most similar with human milk fat. Our data show that an oleaginous yeast can be engineered to produce a human milk fat substitute (β-palmitate), that could be used as an ingredient in infant formulas.