Recent years have seen a tremendous interest in the bottom-up reconstitution of minimal biomolecular systems, with the ultimate aim of creating an autonomous synthetic cell. One of the universal features of living systems is cell growth, where the cell membrane expands through the incorporation of newly synthesized lipid molecules. Here, the gradual tension-mediated growth of cell-sized (≈10 µm) giant unilamellar vesicles (GUVs) is demonstrated, to which nanometer-sized (≈30 nm) small unilamellar vesicles (SUVs) are provided, that act as a lipid source. By putting tension on the GUV membranes through a transmembrane osmotic pressure, SUV–GUV fusion events are promoted and substantial growth of the GUV is caused, even up to doubling its volume. Thus, experimental evidence is provided that membrane tension alone is sufficient to bring about membrane fusion and growth is demonstrated for both pure phospholipid liposomes and for hybrid vesicles with a mixture of phospholipids and fatty acids. The results show that growth of liposomes can be realized in a protein-free minimal system, which may find useful applications in achieving autonomous synthetic cells that are capable of undergoing a continuous growth–division cycle.