Task cooperation is an effective way to execute a complex task in challenging wireless edge networks. Existing TCP/IP-based solutions encounter the problem of low network resource utilization and the heavy dependency of infrastructure connections. Information-centric networking (ICN) is a promising architecture to address these issues. In existing ICN-based task cooperation schemes, the data reuse feature of ICN improves the utilization of network resources, which also brings potential security threats to the reused data. To guarantee the security of data reuse in task cooperation without affecting the data reuse feature, we propose an ICN-based secure task cooperation scheme. In our scheme, the specific naming convention is designed to support task cooperation and the acquisition of keys. In addition, our scheme implements fine-grained access control for data reuse in task cooperation combined with attribute-based encryption. Experimental results show that our scheme enhances the security of task cooperation with low cost compared with existing schemes.