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Almost Schreier domain is an extension of class of pre Schreier domains and b-operation is a type of star operation which is defined for an ideal "A" as an intersection of "AV", where V runs over all valuation over rings of the domain. Here we have studied a domain which is integrally closed and satisfies Almost Schreier property on its b-invertible ideals and call it an almost b- Schreier domain.