Although the traditional physical password, fingerprint unlocking and facial features have improved the security to a certain extent, they have the characteristics of passive authentication and easiness to be stolen. The existing behavioral data collected based on mobile phone sensors is mainly used for human activity recognition and fall detection and health management. Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data. Prophet is robust to missing data and shifts in the trend, and typically handles outliers well. Based on the time series behavior data of mobile terminal users, this paper uses Prophet algorithm to decompose the time series of six kinds of daily behavior and strip off the singular value, to get the inherent cycle and trend of each behavior, and to verify the legitimacy of the behavior user at the next moment. The experimental results on the UniMiB SHAR public dataset show that the user only needs to do 2 cycles of specified actions to realize the prediction of the next time series. The main contribution of this paper is that we propose a new idea for smartphone user authentication. It is based on real-time data of smartphone user behavior, through Phophet algorithm for feature decomposition and time series prediction, and to find the inherent cycle and other characteristics, so as to perform user behavior recognition. This data-driven auxiliary authentication method can effectively solve the problem of easy forgery of static feature recognition such as password, fingerprint and face recognition.