Attribute-based encryption that supports computation outsourcing has been a promising approach to implement fine-grained access control in the Internet of Things (IoT). However, existing outsourcing schemes only focus on minimizing computation on user terminals while overlooking the significant computational burden faced by outsourcing devices. In IoT scenarios with a large volume of concurrent outsourcing requests, such burden can overwhelm outsourcing devices, leading to inefficient decryption execution. This paper, for the first time, proposes ORR-CP-ABE, an outsourced attribute-based encryption scheme with decryption results reuse. In ORR-CP-ABE, users with equivalent access privileges are grouped and issued group-oriented translation keys. Through translation, outsourcing devices can directly reuse previously calculated decryption results of other group members, eliminating redundant outsourced task execution. To further alleviate the burden on outsourcing devices, we use Named Data Networking as the underlying network layer to deploy translation functions and distributed caching for results reuse in the edge network. Furthermore, the reuse behavior in our scheme is configured to be under the control of both the data owner and the initial invoker of results. The security analysis proves the security of ORR-CP-ABE. Performance analysis indicates that it significantly reduces the burden on outsourcing devices and improves decryption efficiency by up to 90% compared to the baseline.