Wireless sensor network(WSN) contains many specially distributed sensors which collect information for people to analyze appointed objects in real-time. WSN is deployed widely in many fields, such as fire detection and remote health care monitoring. User authentication is an important part for the communication of WSN. In 2014, Jiang et al. and Choi et al. proposed their authentication schemes for WSN, respectively. However, we find some weaknesses in them. Jiang et al.'s scheme cannot resist the De-Synchronization attack, the off-line guessing attack and the user forgery attack. Besides, it does not keep the character of strong forward security. Choi et al.'s scheme is under the off-line password guessing attack and the user impersonation attack without user anonymity. We present an improved authentication scheme and prove it to be secure with the formal security model. Also, we analyze the concrete secure characters and the performance of our scheme. Through comparison with some recent schemes, our scheme is more practical and fit for applications.