<p>We investigate the numerical approximation to statistical properties of a periodic solution in distribution to a stochastic differential equation via solving Fokker-Planck equation and analyze the dynamical behavior of its sample trajectories. We propose a novel approximation framework to approach the density function of the periodic solution in distribution via seeking the time periodic solution to the corresponding Fokker-Planck equation. Specifically, we first truncate the spatial variable onto a finite domain, and then introduce a time periodic condition and a phase condition to construct a well-posed extending equation, whose solution is an approximation to the density function. We then discretize the extending equations using finite difference method and obtain the second and first order convergence rate under certain conditions. We also apply the large deviation theory to analyze the dynamical property of sample trajectories of the periodic solution in distribution and find that most of the sample trajectories exhibit almost periodic behavior, while the probability of rest trajectories is exponentially small. To our best knowledge, studying the dynamics of trajectories of a periodic solution in distribution using large deviation theory has never been proposed in the literature. Finally, we present several numerical experiments to illustrate our theoretical analysis.</p>