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Public key encryption is an important method to ensure data security. In recent years, researchers have designed multiple certificateless encryption (CLE) schemes, and the security proofs of most known schemes are done in random oracle model (ROM). It is generally known that the standard model (SM) is more reliable than the ROM. Currently, there are only three CLE schemes with provable security in SM. Unfortunately, all three schemes require pairing operations, enjoy high computation costs, and are not suitable for mobile devices. In this paper, we constructed a new CLE scheme. Compared with other schemes, the new scheme is with two advantages: First, the security proofs of the new scheme are done in SM. Second, the new scheme does not use pairing operation and enjoys higher computation efficiency. Efficiency analysis shows that the computation cost of the new scheme is only 12.4% of that of the most efficient scheme known, which is suitable for mobile devices. [ABSTRACT FROM AUTHOR]