Smart phones are widely used in our daily life on which there are much personal and sensitive information. To prevent information disclosure and to strengthen the authentication security for smartphones, implicit methods for authentication attract people's attention. Implicit authentication (IA) can continuously authenticate users by profiling their behavior using the variety of sensors prevalent. IA requires no explicit user action, which is much more user-friendly. In this paper, we focus on characteristic distribution probability evaluation for key-stroke dynamics and propose an authentication method based on Jensen-Shannon divergence(JS-divergence). Two phases, training phase and authentication phase, are used to identify the true user in our method. For authentication phase, the set of behavioral characteristics is preprocessed as the behavior characteristic distribution probability vector(BCDPV) to obtain the JS-divergence between two sets of behavioral characteristics. For training phase, a novel update strategy for training set based on sliding window is proposed, which can overcome the difficulties of retraining. The security of this method is estimated by False Rejection Rate (FRR), False Acceptance Rate (FAR) and Equal Error Rate(ERR). The result shows that the size of the training set (i.e. the size of the sliding window) is not the bigger the better and 5 for the best results. It also shows that our method based on JS divergence works better than that based on other measurement methods such as the cosine, chebyshev and correlation Euclidean.