  Here we continue to characterize a recently introduced notion, le-modules
$_{R}M$ over a commutative ring $R$ with unity \cite{Bhuniya}. This article
introduces and characterizes Zariski topology on the set $Spec(M)$ of all prime
submodule elements of $M$. Thus we extend many results on Zariski topology for
modules over a ring to le-modules. The topological space Spec(M) is connected
if and only if $R/Ann(M)$ contains no idempotents other than $\overline{0}$ and
$\overline{1}$. Open sets in the Zariski topology for the quotient ring
$R/Ann(M)$ induces a base of quasi-compact open sets for the Zariski-topology
on Spec(M). Every irreducible closed subset of Spec(M) has a generic point.
Besides, we prove a number of different equivalent characterizations for
Spec(M) to be spectral.
