In this paper, we are going to define Neutrosophic Boolean rings and study their algebraic structure. A finite Boolean ring satisfies the identity for all , which implies the identity for each positive integer . With this as motivation, we consider a Neutrosophic Boolean ring which fulfils the identity for all and describes several Neutrosophic rings which are Neutrosophic Boolean rings with various algebraic personalities. First, we show a necessary and sufficient condition for a Neutrosophic ring of a classical ring to be a Neutrosophic Boolean ring. Further, we achieve a couple of properties of Neutrosophic Boolean rings satisfied by utilizing the Neutrosophic self-additive inverse elements and Neutrosophic compliments.