The objective of this article is to introduce a new hybrid model of neutrosophic N-soft set which is combination of neutrosophic set and N-soft set. We introduce some basic operations on neutrosophic N-soft sets along with their fundamental properties. For multi-attribute decisionmaking (MADM) problems with neutrosophic N-soft sets, we propose an extended TOPSIS (technique based on order preference by similarity to ideal solution) method. In this method, we first propose a weighted decision matrix based comparison method to identify the positive and the negative ideal solutions. Afterwards, we define a separation measurement of these solutions. Finally, we calculate relative closeness to identify the optimal alternative. At length, a numerical example is rendered to illustrate the developed scheme in medical diagnosis via hypothetical case study.