In this paper we introduced new types of open and closed sets in Quad-topological spaces, where we have introduced the definition of open sets of the pattern N and closed sets of the pattern N in Quad-topological spaces, as the we know from the open sets of the pattern S and closed sets of the pattern S in these spaces, and we studied the basic properties of these new types of sets, as the we have created the relationship between them and open sets and closed in these Quad-topological spaces. Then use this new concept of open and closed sets in the definition of closure and interior set, where we know the closure and interior set of the pattern N by relying on these new varieties of open and closed sets, we also found the basic properties of closure and the interior of the pattern N.