The objective of this paper is to introduce and study the notion of neutrosophic subtraction algebras and neutrosophic subtraction semigroups. It also introduces the notion of neutrosophic ideals of neutrosophic subtraction semigroup and presents some of their basic properties. In addition, the notion of neutrosophic homomorphism of neutrosophic subtraction semigroups and neutrosophic quotient subtraction semigroups was also introduced.