Abstract: The concept of vague set is applied to B-algebras and the notions of vague B-algebra, vague normal set and vague normal B-algebra are defined. And the properties and relations in between are discussed. Some properties of the homomorphic image and inverse image of vague B-algebra (resp. vague normal set, vague normal B-algebra) are examined. The intersection of vague ideals (resp. vague normal sets, vague normal B-algebras) are investigated.