  In this paper we prove that the anti-canonical bundle of a holomorphic
foliation $\mathcal{F}$ on a complex projective manifold cannot be nef and big
if either $\mathcal{F}$ is regular, or $\mathcal{F}$ has a compact leaf. Then
we address codimension one regular foliations whose anti-canonical bundle is
nef with maximal Kodaira dimension.
