  In this paper we introduce the class of graded Poisson color algebras as the
natural generalization of graded Poisson algebras and graded Poisson
superalgebras. For $\Lambda$ an arbitrary abelian group, we show that any of
such $\Lambda$-graed Poisson color algebra $\mathcal{P}$, with a symmetric
$\Lambda$-support is of the form $\mathcal{P} = \mathcal{U}\oplus\sum_j I_j$,
with $\mathcal{U}$ a subspace of $\mathcal{P}_1$ and any $I_j$ a well described
graded ideal of $\mathcal{P},$ satisfying $\{I_j, I_k\}+I_j I_k=0$ if $j\neq
i.$ Furthermore, under certain conditions, the gr-simplicity of $\mathcal{P}$
is characterized and it is shown that $\mathcal{P}$ is the direct sum of the
family of its graded simple ideals.
