Dissipative particle dynamics (DPD) simulations are employed to study the shape transformations of vesicles formed from amphiphilic triblock copolymers. The amphiphilic molecule is built front two different hydrophilic blocks on the sides and a hydrophobic block in the middle. To model the asymmetric membrane in the vesicle, spontaneous curvature is introduced by the difference in repulsive parameters between the two different hydrophilic blocks of the amphiphilic molecule. A plethora of complex vesicle shapes is revealed by the DPD simulations, including some shapes that have not been reported in other simulation studies on vesicles, such as starfish-shaped, toroidal, long rodlike, and inverted vesicles. These simulated vesicles agree with theoretically derived vesicle shapes based on the spontaneous curvature model and also with experimental observations.