  In this paper, firstly, for some $4n$-dimensional almost complex manifolds
$M_{i}, ~1\le i \le \alpha$, we prove that $\left(\sharp_{i=1}^{\alpha}
M_{i}\right) \sharp (\alpha{-}1) \mathbb{C} P^{2n}$ must admits an almost
complex structure, where $\alpha$ is a positive integer. Secondly, for a
$2n$-dimensional almost complex manifold $M$, we get that $M\sharp
\overline{\mathbb{C} P^{n}}$ also admits an almost complex structure. At last,
as an application, we obtain that $\alpha\mathbb{C} P^{2n}\sharp
\beta\overline{\mathbb{C} P^{2n}}$ admits an almost complex structure if and
only if $\alpha$ is odd.
