In this paper, we extend the N-compactness in L-Fuzzy Topological space to intuitionistic L-Fuzzy Topological space. Firstly, intuitionistic fuzzy N-compactness is defined by α-quasi-coincident family in an intuitionistic L-Fuzzy Topological space, and its equivalent characterization is given by using intuitionistic fuzzy α-net and intuitionistic fuzzy filter. Secondly, it is proved that intuitionistic fuzzy N-compactness has closed heritability; The union of a finite number of intuitionistic fuzzy N-compact sets is still intuitionistic fuzzy N-compact set and intuitionistic fuzzy N-compactness is topological invariance. This research enriches the theoretical system of intuitionistic L-fuzzy Topological space, and provides a certain reference value for the related theoretical research of intuitionistic L-fuzzy Topological space.