  Let $X$ be a compact generalized Sasakian CR manifold of dimension $2n-1$,
$n\geqslant2$, and let $L$ be a generalized Sasakian CR line bundle over $X$
equipped with a rigid semi-positive Hermitian fiber metric $h^L$. In this paper
we prove that if $h^L$ is positive at some point of $X$ and conditions Y(0) and
Y(1) hold at each point of $X$, then $L$ is big.
