The objective of this paper is to formally present the concept of NeutroGroups by considering three Neutro Axioms (Neutro Associativity,existence of Neutro Neutral element and existence of Neutro Inverse element). Several interesting results and examples of Neutro Groups, Neutro Subgroups, Neutro Cyclic Groups, Neutro Quotient Groups and Neutro Group Homomorphisms are presented. It is shown that generally, Lagrange’s theorem and 1st isomorphism theorem of the classical groups do not hold in the class of Neutro Groups.