Soft set developed by Smarandache in 2018 to Hypersoft set (HSS) to deal with multiargument approximate functions. The soft set cannot deal with cases when attributes are required to be further divided into disjoint attribute-valued sets. Neutrosophic Hypersoft Set (NHSS) is the most effective and useful method to handle the environment which involved more than one attribute. Neutrosophic Hypersoft Set introduced by combining Hypersoft Set and Neutrosophic Soft Set. In this paper, we first define the concept of Possibility Neutrosophic Hypersoft Set (PNHSS in short) which is combination of PNSS and HSS. Certain essential basic characteristics as subset, equal and complement are studied with illustrative examples. Basic operations such as: union, intersection and some properties such as commutative, associative, distributive low and De Morgan’s low are discussing. Also, we introduce AND and OR operation of PNHSS with suitable examples and some propositions.