In security analyses of authentication protocols for smart cards, we usually consider two possible attacks: replay attacks and active attacks. The aims of both attacks are to try to use fake cards for successful authentication. In addition to these attacks, there are other possible attacks, the aim of which is only to let the valid cards to be unsuccessfully authenticated. These attacks are referred to as hostile attacks. The smart card authentication protocols may face a challenge of not functioning properly with the hostile attacks, the replay attacks and active attacks. In this paper, we proposed an improved authentication protocol by modifying a classic unilateral asymmetric authentication protocol to provide a strong protection to prevent the smart cards from these three kinds of attacks. The security analyses show that the improved authentication protocol is much stronger against these three kinds of attacks than the traditional protocol.