Behavioral-biometric based authentication schemes on mobile phones usually begin by establishing a normal-behavioral model using machine learning classifiers and then identify behavioral anomalies through comparing current behavioral events with the established model. If an anomaly is detected, this kind of schemes will require the user for validation (i.e., input correct PIN). In this paper, we first propose a lightweight touch-dynamics-based user authentication scheme on a touchscreen mobile phone, which consists of only 8 touch-gesture related features. In addition, we further design an adaptive mechanism that can periodically select a better classifier to maintain the authentication accuracy during user authentication. As a study, we implement a cost-based metric that enables this mechanism to choose a less costly classifier. In the evaluation, the experimental results of involving 50 participants indicate that our proposed user authentication scheme can achieve an average error rate of 2.46% and that the adaptive mechanism can maintain the authentication accuracy at a relatively stable level.