The aim of this work was to test the utility of the Hansen theory to predict the best cosolvent for supercritical carbon dioxide (sc-CO2) to reach the selective extraction of fatty acids from Tetraselmis suecica. The order in the cosolvent power was established with five organic solvents used in food production: acetone, diethyl ether, ethanol, n-hexane and methanol. Predictions focused on the selective extraction of oleic, linoleic and a-linolenic acid. The cosolvent power depended on the fatty acid, but in general, the best cosolvent for the three target compounds was ethanol. Predictions were validated through equilibrium data and extraction yields from T. suecica. Operating at 305.15 K and 20 MPa, the extracted oil with the sc-CO2-ethanol (5 % mass fraction) mixture significantly improved the content of the target fatty acids compared with pure sc-CO2; e.g. the a-linolenic acid content was 16 % in the oil obtained with pure sc-CO2 while it was 25 % in the oil obtained with sc-CO2 + 5 % ethanol. However, the Hansen theory predicted that the miscibility enhancement of the fatty acids caused by increasing ethanol concentrations in the supercritical solvent mixture was not progressive. In fact, at high pressures and high ethanol concentrations, it was predicted up to less than half the miscibility enhancement.