An essential step of nanoliposome formation in an aqueous lipid solution is the transition from discoidal lipid aggregate (bicelle) to vesicle. We investigate here the bicelle-to-vesicle transition of a binary lipid mixture of saturated and unsaturated phosphatidylcholine by performing nonequilibrium molecular dynamics simulations with the coarse-grained representation of di-palmitoyl-phosphatidyl-choline (DPPC) and di-linoleoyl-phosphatidyl-choline (DLiPC). When the DPPC molecules of a stable DPPC bicelle are randomly replaced with the DLiPC molecules, the transition occurs for higher apparent DLiPC concentrations. On the other hand, when the DPPC molecules only in the core region of the bicelle are replaced, the transition occurs even for lower apparent DLiPC concentrations. For the bicelle where the head and tail layers are pure DPPC and DLiPC monolayers, respectively, the side of the DLiPC monolayer becomes the concave surface of bending bicelle. Controlling the local lipid compositions in a binary lipid bicelle has the potential to determine the success of vesicle formation and the direction of bicelle bending. Our findings help explain nanoliposome formation with sonication and give useful information for controlling encapsulation efficiencies of nanoliposomes.