  In this article, we study almost cosymplectic manifolds admitting
quasi-Einstein structures $(g, V, m, \lambda)$. First we prove that an almost
cosymplectic $(\kappa,\mu)$-manifold is locally isomorphic to a Lie group if
$(g, V, m, \lambda)$ is closed and on a compact almost
$(\kappa,\mu)$-cosymplectic manifold there do not exist quasi-Einstein
structures $(g, V, m, \lambda)$, in which the potential vector field $V$ is
collinear with the Reeb vector filed $\xi$. Next we consider an almost
$\alpha$-cosymplectic manifold admitting a quasi-Einstein structure and obtain
some results. Finally, for a $K$-cosymplectic manifold with a closed,
non-steady quasi-Einstein structure, we prove that it is $\eta$-Einstein. If
$(g, V, m, \lambda)$ is non-steady and $V$ is a conformal vector field, we
obtain the same conclusion.
