We have investigated the dynamics of nano-meter-sized domains on a vesicle composed of saturated phospholipids, unsaturated phospholipids and cholesterols by means of a neutron spin echo technique. The diffusion coeffisient of the domains obtained from the intermediate scattering function is about two orders of magnitude larger than that calculated by Saffman and Delbrück law. From molecular dynamics simulations we found another type of the domain dynamics where the domains are agitated by thermal fluctuation and repeats coalescence and rupture. The relaxation rate of the new mode is about two orders of magnitude larger than that of the diffusion mode. The coalescence and rupture mode of domains may be responsible for the observed domain dynamics.