In this talk, we introduce optmal transport on finite graphs. The probability set forms a Riemannian manifold wiht a Wasserstein metric on finite graphs recently introduced. We call it probability manifold. Various developments related to the probability manifold, e.g., Fokker-Planck equation and Hamilton-Jacobi equation with be sketched. Their connections with Shannon-Boltzmann entropy and Fisher information on graphs will also be considered.