The transition of copper oxide thin films from CuO to Cu2O during vacuum annealing has been studied by transmission electron microscopy and Rutherford backscattering spectroscopy. Dark field images show that isolated and large Cu2O grains emerge from the small CuO grain matrix. The abrupt change in oxygen concentration across the phase boundary between CuO and Cu2O in the reaction is different from the continuous change of in oxidation and reduction of the superconducting YBa2Cu3O7- oxide. The growth of Cu2O grains is linear with time and has an activation energy of 1.1 eV. We propose that the discontinuous morphology of grain growth of Cu2O is due to the migration of the Cu2O-CuO phase boundary induced by oxygen out-diffusion along the moving phase boundary.