To reduce a user’s decryption cost and protect the private information from being leaked, Green et al. proposed an approach our sourcing the decryption of the attribute based encryption (ABE) scheme to the cloud server. Later, almost all ABE schemes with outsourced decryption (ABE-OD) used their model or approach. However, the cloud server needs to repeat the outsourced decryption service of the same ciphertext for distinct users satisfying the same access policy in these schemes. Green computing is the atmosphere conscientious and recyclable utilization of resources. The green cloud networks can reduce their cost or energy requirements by adapting its performance, optimizing resources management and services. The method is not efficient for the cloud server in the green cloud networks. In this project, to take into account recyclable utilization of resources for the cloud server, we put forward a new and secure approach to reduce total overhead of the cloud server when many users satisfying an access policy require the outsourced decryptions for the same ciphertext besides decreasing the decryption computation cost for users. Compared with the existing ABE-OD schemes, our total overhead of the cloud server is independent of the number of the users who satisfy an access policy and request the outsourcing decryption service. Finally, we extend our approach to a RCCA-secure ABE-OD scheme.