The aim of the study is to introduce a neutrosophic N −subalgebra and neutrosophic N −ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N −subalgebra (neutrosophic N −ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N −subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N −ideal of a Sheffer stroke BCH-algebra is its neutrosophic N −subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N −ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N −functions on this algebraic structure and some properties are investigated.