In this paper we extend fuzzy analytic hierarchy process into neutrosophic cubic environment. The neutrosophic cubic analytic hierarchy process can be used to manage more complex problems when the decision makers has a number of uncertainty, assigning preferences values to the considered object. We also define the concept of triangular neutrosophic cubic numbers and their operations laws. The advantages of the proposed methodology and the application of neutrosophic cubic analytic hierarchy process in decision making are shown by testing the numerical example in practical life. Manuscript profile