  In this paper, we introduce the notion of differential graded Poisson algebra
and study its universal enveloping algebra. From any differential graded
Poisson algebra $A$, we construct two isomorphic differential graded algebras:
$A^e$ and $A^E$. It is proved that the category of differential graded Poisson
modules over $A$ is isomorphic to the category of differential graded modules
over $A^e$, and $A^e$ is the unique universal enveloping algebra of $A$ up to
isomorphisms. As applications of the universal property of $A^e$, we prove that
$(A^e)^{op}\cong (A^{op})^e$ and $(A\otimes_{\Bbbk}B)^e\cong
A^e\otimes_{\Bbbk}B^e$ as differential graded algebras. As consequences, we
obtain that ``$e$'' is a monoidal functor and establish links among the
universal enveloping algebras of differential graded Poisson algebras,
differential graded Lie algebras and associative algebras.
