Attribute-based encryption (ABE) is a new cryptographic primitive which provides a promising tool for addressing the problem of secure and fine-grained data sharing and decentralized access control. Key-policy attribute-based encryption (KP-ABE) is an important class of ABE, where cipher texts are labeled with sets of attributes and private keys are associated with access structures that control which cipher texts a user is able to decrypt. KP-ABE has important applications in data sharing on untrusted cloud storage. However, the cipher text size grows linearly with the number of attributes embedded in cipher text in most existing KP-ABE schemes. In this paper, we describe our work on designing a KP-ABE scheme with constant size cipher text for monotonic access structures. The downside of the proposed KP-ABE scheme is that private keys have multiple size growth in the number of attributes in the access structure. The proposed KP-ABE scheme is proved to be secure under the general Diffie-Hellman exponent assumption.