In this talk, I will discuss a relationship between the K-stability and the Calabi's extremal metrics on toric manifolds. We prove that on a polarized toric manifold the relative K-stability is a necessary condition for the existence of Calabi's extremal metrics, and also we show that the modified K-energy is proper in the space of G_0-invariant Kähler metrics for the case of toric surfaces which admit the extremal metrics. If possible I will also discuss an existence theorem for the weak extremal metrics on toric manifolds.