Identity-based encryption with equality test supporting flexible authorization (IBEET-FA) allows the equality test of underlying messages of two ciphertexts while strengthens privacy protection by allowing users (identities) to control the comparison of their ciphertexts with others. IBEET by itself has a wide range of useful applicable domain such as keyword search on encrypted data, database partitioning for efficient encrypted data management, personal health record systems, and spam filtering in encrypted email systems. The flexible authorization will enhance privacy protection of IBEET. In this paper, we propose an efficient construction of IBEET-FA system based on the hardness of learning with error (LWE) problem. Our security proof holds in the standard model.