To resist existing limitations and associated attack by anonymization of single sensitive attributes, an ( α _ij, k,m)-anonymity model based on greedy algorithm was proposed. Firstly, the ( α _ij, k,m)-anonymity model was mainly to protect multi-sensitive attribute information. Secondly, the model for level was carried out according to the sensitive values of the sensitive attributes, if there were m sensitive attributes, there were m tables. Thirdly, each level was assigned a specific account α _ij by the model. Finally, the ( α _ij, k,m)-anonymity algorithm based on greedy strategy was designed, and a local optimum method was adopted to implement the ideas of the model which improves the degree of data privacy protection. The proposed model was compared with other three models from information loss, execution times, and the sensitivity distance of equivalent class. The experimental results show that, although the execution time of the proposed model is slightly longer than other compared models, however, the information loss is less and the privacy protection degree of data is higher. It can resist the associated attack and protect the data of multi-sensitive attributes.