In this talk, I will present deformations of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's analytic deformation theory and extend their "Theorem of existence" for deformations of complex structures in the context of holomorphic Poisson deformations. I will discuss infinitesimal version of deformations of compact holomorphic Poisson manifolds and describe a differential graded Lie algebra governing holomorphic Poisson deformations of a compact holomorphic Poisson manifold in the language of "functor of Artin rings.