We present an energy stable fully discrete discontinuous Galekin(DG)finite element method for the thin film epitaxy problem.Based on the method of lines,we construct and prove the energy stability of the spatial semi-discrete DG scheme firstly.The energy stability of the fully discrete convex splitting DG scheme is also proved.To improve the temporal accuracy,spectral deferred correction(SDC)method is adapted to achieve the high order accuracy in space and time.