Community detection algorithms can reveal the underlying structure of networks and simplify network analysis. However, as these algorithms develop, concerns about the over-mining of individual information have arisen. To address this, the concept of Community Detection Attack (CDA) has been proposed to protect privacy by hiding community structures through minor rewiring of connections. However, most existing community detection attack algorithms select target nodes based on specific node characteristics. As many real-world networks exhibit power-law properties, this often leads to target nodes concentrating within certain communities, potentially limiting the diversity and scope of the attack. To this end, we propose a community detection attack algorithm based on balanced budget allocation (CDA-BBA), which distributes the attack budget across multiple key communities before selecting target nodes. This avoids concentrating the attack on just a few communities, making target nodes more dispersed and enhancing global attack effectiveness. Additionally, we suggest a new attack strategy to effectively alter the community structure. We evaluate the proposed CDA-BBA against five community detection algorithms on nine datasets by comparing it with six state-of-the-art methods. The experimental results show that the proposed algorithm CDA-BBA performs well in both attack effectiveness and time efficiency.