Abstract: A sampling trajectories-Monte Carlo method for solving non-Markovian Langevin equation driven by harmonic colored noise and with memory-damped is presented based on increased of four-dimensional phase space. The activation rates for the case of impurity diffusion in the host crystalline solid are calculated. An initial distribution of colored noise overlooked in the past for getting stationary correlation of random force is derived. The stochastic resonance phenomenon by expressed theoretically is better shown.