Hyperstructure theory has many applications to several areas of pure and applied sciences. This paper investigates some properties of hyper B -algebras which is a generalization of B -algebras. This paper also introduces the notion of hyper B -ideals, weak hyper B -ideals and strong hyper B -ideals in hyper B - algebras and gives some relations among these hyper B -ideals. Relations between hyper B -ideals and subhyper B -algebras of H is also discussed. Moreover, homomorphism on hyper B -algebra is defined and some related properties are given. Finally, proof of the relationship between the hyper B -algebras and hypergroups is provided.