Most remote user authentication schemes are designed by encryption or hash-function techniques. In terms of computational cost, the hash-function-based scheme is more simple and efficient. In 2008, under the conditions of using tamper-resistant smart card device and the verifier table storage technique, Chen-Lee proposed a novel mutual authentication protocol using hash function to solve remote user authentication. Based on Chen-Lee scheme, a secure and efficient mutual authentication protocol using hash function is proposed. The proposed scheme not only keeps the advantages of Chen-Lee scheme, but also avoids using well-defined tamper-resistant smart card device and storing the verifier table in server.