  In this paper, we studied the map defined by a non-very ample line bundle on
some special irregular varieties. As to this topic, it is well known that for a
line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base
point free, and 3L is very ample, moreover the map defined by the linear system
$|2L|$ is well understood (cf. Theorem \ref{oldth}). First, we generalized this
classical result to projective bundles over Abelian varieties (cf. Theorem
\ref{key}). Then we studied the bicanonical map of an irregular primitive
variety $X$ of general type with $dim(X) = q(X)$, in fact we got a relation
between the map and the reducibility of a divisor.
