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Publishing the data with multiple sensitive attributes brings us greater challenge than publishing the data with single sensitive attribute in the area of privacy preserving. In this paper, we propose a novel privacy preserving model based on k-anonymity called (α, β, k)-anonymity for databases. (α, β, k)-anonymity can be used to protect data with multiple sensitive attributes in data publishing. Then, we set a hierarchy sensitive attribute rule to achieve (α, β, k)-anonymity model and develop the corresponding algorithm to anonymize the microdata by using generalization and hierarchy. We verify (α, β, k)-anonymity approach can effectively protect privacy information of individual and resist background knowledge attack in publishing the data with multiple sensitive attributes by specific example.