ABE is a relatively recent approach that reconsiders the concept of public-key cryptography. It basically provides access to a document if and only if the user attributes (e.g. Email ID, DOB or the country he lives in) satisfies the access policy defined by the owner of the document. Access policy is the combination of attributes (generally defined using AND/OR logical operations) using which the document can be decrypted. One of the main efficiency drawbacks of the existing ABE schemes is that decryption involves expensive pairing operations and the number of such operations grows with the complexity of the access policy. Recently proposed ABE system with outsourced decryption largely eliminates the decryption overhead of server. In such system, the proxy server such as cloud service provider is present which has a transformation key. Any cipher text encrypted using ABE with outsourced decryption scheme into a simple cipher text. This intermediate cipher text can be transformed into plaintext by proxy server. This process incurs a small computational overhead. Security of an ABE system with outsourced decryption ensures that an adversary (including a malicious proxy) will not be able to learn anything about the encrypted message; however, it does not guarantee the correctness of the transformation done by the cloud. We also consider a new requirement of ABE with outsourced decryption: verifiability. Informally, verifiability guarantees that a user can efficiently check if the transformation is done correctly. We give the formal model of ABE with verifiable outsourced decryption.