  An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs
is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$
such that all $n$ oriented vertex sums are pairwise distinct, where an oriented
vertex sum is the sum of labels of all arcs entering that vertex minus the sum
of labels of all arcs leaving it. A graph $G$ has an antimagic orientation if
it has an orientation which admits an antimagic labeling. Hefetz, M{\"{u}}tze,
and Schwartz conjectured that every connected graph admits an antimagic
orientation. In this paper, we show that every bipartite graph without both
isolated and degree 2 vertices admits an antimagic orientation and every graph
$G$ with $\delta(G)\ge 33$ admits an antimagic orientation. Our proof relies on
a newly developed structural property of bipartite graphs, which might be of
independent interest.
