Ostwald ripening refers to a process of a particle/droplet/bubble system under thermal equilibrium state adjusting the size distribution spontaneously to reduce the total surface energy. With knowing lack in numerical studies, a lattice Boltzmann approach is used to simulate the ripening process of two dimensional vapour bubble cluster dominated by phase transition kinetics. By comparing the numerical results with the theoretical prediction derived in two dimensional space, it is shown that the lattice Boltzmann method is accurate in the simulations. The results also indicate that the mass transfer in liquid phase is driven by hydrodynamic pressure distribution and the hydrodynamic collapse of bubbles influences the size distribution function in small size region. The impact of the parameters of the equation of state of the material is studied further. A positive relation between phase transition speed and specific internal energy is proposed, which enhances the thermal fundamental of phase transition.