In this paper, we study the concept of an n-prime ideal in 0-distributive lattices. The characterization of minimal n-prime ideals is obtained. Further, the topology on the set $\mathcal {P}_{n}(L)$ of minimal n-prime ideals of a 0-distributive lattice L is studied and it is shown that $\mathcal {P}_{n}(L)$ is compact if and only if it is finite.