  In this paper, we give a description of holomorphic multi-vector fields on
smooth compact toric varieties, which generalizes Demazure's result of
holomorphic vector fields on toric varieties. Based on the result, we compute
the Poisson cohomology groups of holomorphic toric Poisson manifolds, i.e.,
toric varieties endowed with $T$-invariant holomorphic Poisson structures.
