  In this note we studied the primitive varieties of general type with $q(X) =
dim(X)$ and non-birational bicanonical maps. Let $X$ be such a variety. We
bounded the degree of its bicanonical map. If moreover the Albanese variety
$Alb(X)$ is simple, we proved that the Euler number $\chi(\omega_X) = 1$, and
$|2K_X|$ separates the points mapped to the same general point via the Albanese
map.
