The aim of this paper is to propose an algorithm to solve and enhance a multi-level multi-objective integer quadratic programming problem (MLMOIQPP) under a single-valued Pentagonal Neutrosophic environment applied to the objective functions. The suggested solution takes advantage of multi-objective optimization in addition to the fuzzy approach as well as the branch and bound technique, which is implemented at each decision level to develop a generalized maximization-minimization model for obtaining the integer satisfactory solution after applying the score and accuracy function in the first phase of the solution methodology to singlevalued Pentagonal Neutrosophic parameters to be converted into an equal crisp form. An illustrative example is demonstrated to validate the proposed solution algorithm.