A huge amount of information in social network has accumulated into a kind of big graph data. Generally, to prevent privacy leakage, the data to be published need to be anonymized. Most of the existing anonymization scheme cannot prevent such attacks by background knowledge of both structure and attribute information among nodes. To address the issue, this investigation proposes a clustering-anonymization method for attribute-graph based on link edges and attributes value among nodes. Firstly, the data in the social network is represented by attribute graph. Then all the nodes of this attribute graph are clustered into certain super-nodes according to structural and attribute similarity between two nodes, each of which contains no less than k nodes. Finally, all the super-nodes are anonymized. In this method, the structure masking and attribute generalization for every super-nodes can respectively prevent all the recognition attacks by background knowledge of goals' linkages and attribute information. In addition, it balances the closeness of links among nodes and proximity of attributes value during clustering, therefore can reduce the total loss of information triggered by masking and generalization to maintain the availability of these graph data. Experiment results also demonstrate the approach achieves great algorithm performance and reduces information loss remarkably.