In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){setminus}int;V(a)$.