We report here a controllable shape transformation of polymer vesicles (polymersomes) constructed from block copolymers of which the hydrophobic part is a high-molecular-weight glassy segment. Control over the shape transformation is obtained by kinetic manipulation of the phase behavior of this glassy hydrophobic segment. Kinetic manipulation of the phase behavior of polymer membranes allows for different shapes of polymersomes to be captured at specific times, which directly translates into physically robust nanostructures that are otherwise unobtainable. Combining the morphological diversity of giant liposomes and the physical robustness of polymersomes, our finding can be a general way to realize unusual nanostructures in a predictable manner.