Using the three dimensional (3D) Ising model with Metropolis algorithm, we simulate the evolution from nonequilibrium to equilibrium at zero magnetic field near the critical temperature Tc. To quantify the relaxation time of different processes, the average relaxation time is introduced. It is shown that the average relaxation time is related to system size, temperature and initial configuration. The first four cumulants of order parameter during the nonequilibrium evolution are presented. They all deviate from corresponding equilibrium expectations. In particular, the sign of the third and the forth cumulants could be either positive or negative, depending on the observation time. These features at T > Tc are consistent with the results obtained from dynamical models. At T < Tc, the evolution of nonequilibrium lasts much longer, and the influence is much larger in comparison with that at T > Tc.