Abstract: The vesicle membranes, formed by bilayers of lipid molecules, are simple forms of biological membranes which exist everywhere in life and compartmentalize living matter into cells and subcellular structures, and are essential for many biological functions. The equilibrium and transition shapes of bilayer vesicle membranes have been successfully modeled via a phase field formulation of certain shape energy. Adaptive meshing technique is applied to the corresponding minima/saddle searching dynamics of the phase functions, which significantly improves the efficiency of the phase field simulation and enhances its capability in handling complex shape and topological changes. The effectiveness of the adaptive method is demonstrated through numerical examples.