We study conjunctive keyword search scheme allowing for remote search of data containing each of several keywords on encrypted data storage system. A data supplier first uploads encrypted data on a storage system, and then a user of the storage system searches data containing keywords over encrypted data hence insider (such as an administrator of the storage system) and outsider attackers do not learn anything else about the data. Recently, Golle et al. first suggested conjunctive keyword search scheme, but the communication and storage costs linearly depend on the number of stored data in the database, hence it is not really suitable for a large scale database. In this paper, we propose an efficient conjunctive keyword search scheme over encrypted data in aspects of communication and storage costs. Concretely, we reduce the storage cost of a user and the communication cost between a user and a data supplier to the constant amounts. We formally define security model for a conjunctive keyword search scheme and prove that the proposed scheme is secure under the decisional bilinear Diffie-Hellman (DBDH) assumption in the random oracle model.