Attribute-based encryption allow user to encrypt data using public-key then it decrypt data using private-key in the cloud. ABE provide the public-key one-to-many encryption. Access polices and user attributes are associated with private keys and ciphertexts. The drawbacks of the existing ABE schemes are that decryption involves expensive pairing operations, the number of such operations grows with the complexity of the access policy and the transformations are performed only in the data. Recent ABE system with outsourced decryption largely eliminates the decryption overhead for users. Security of that system ensures that an adversary, it guarantee the correctness of the transformation done by the cloud. In this paper, we consider a new requirement of ABE with enforced triple DES. In our scheme the triple DES is applied to the cloud environment because it provides the additional security by applying symmetric key encryption to the key. This model of ABE with verifiable outsourced decryption and propose a concrete scheme. We prove that our new scheme is both secure and verifiable, without relying on random oracles. Finally, we show an implementation of our scheme and result of performance measurements.