  A $labeling$ of a digraph $D$ with $m$ arcs is a bijection from the set of
arcs of $D$ to $\{1,2,\ldots,m\}$. A labeling of $D$ is $antimagic$ if no two
vertices in $D$ have the same vertex-sum, where the vertex-sum of a vertex $u
\in V(D)$ for a labeling is the sum of labels of all arcs entering $u$ minus
the sum of labels of all arcs leaving $u$. An antimagic orientation $D$ of a
graph $G$ is $antimagic$ if $D$ has an antimagic labeling. Hefetz,
M$\ddot{u}$tze and Schwartz in [J. Graph Theory 64(2010)219-232] raised the
question: Does every graph admits an antimagic orientation? It had been proved
that for any integer $d$, every 2$d$-regular graph with at most two odd
components has an antimagic orientation. In this paper, we consider the
2$d$-regular graph with many odd components. We show that every 2$d$-regular
graph with any odd components has an antimagic orientation provide each odd
component with enough order.
