In this paper, the authors present a kind of generalized least general generalization, called MGG (multiple minimum general generalization), under generalized θ-subsumption. MGG does effectively reduce the generalization of inductive hypotheses to extent, such that the problem of over-generalization is satisfactorily overcome. For computing MGG efficiently, the relation between normal generalization and MGG is studied and an algorithm CMGG (clustering-based multiple minimum general generalization) based on concept clustering is proposed, which can effectively figure out MGG and reflect accurately the internal relation of the set of learning examples.