The main purpose of the paper is to introduce the notion of complex interval neutrosophic soft set (CIVNSS) theory, which is the generalization of the soft set, fuzzy soft set, interval-valued fuzzy soft set, interval neutrosophic soft set ,etc to describe the uncertain time-periodic phenomena in the form of an interval. After that, some important properties and operations on CIVNSSs have been discussed. Also, we study the similarity measures on CIVNSSs. Then, an algorithm has been constructed by using the CIVNSS aggregate operator. Finally, to show the impact of CIVNSS in solving real decision-making problems, an example, which is suitable to the current theory, is chosen, which ensures the effectiveness of the proposed theory in group decision-making problem.