In this paper, we propose a new efficient scheme to outsource the the decryption of attribute based encryption with energy efficiency. We observe all the previous work on out-sourcing the decryption of ABE cares little about the ciphertext length. Almost all of them have linear length ciphertext with the attributes or the policy. But we know that transferring so long ciphertexts via wireless network for mobile phone can easily run out the energy of the battery, which hesitates the adaption of these solutions in actual scenarios. In this paper, we propose a new scheme to outsource the decryption of ABE but with constant size ciphertexts, which can achieve high energy efficiency. Compared with the pervious work on outsourcing the decryption of ABE, our work can achieve high energy efficiency and low bandwidth for the mobile phone users.