The battery power state (SOP) is the basic indicator for the Battery management system (BMS) of the battery energy storage system (BESS) to formulate control strategies. Although there have been many studies on state estimation of lithium-ion batteries (LIBs), aging and temperature variation are seldom considered in peak power prediction during the whole life of the battery. To fill this gap, this paper aims to propose an adaptive peak power prediction method for power lithium-ion batteries considering temperature and aging is proposed. First, the Thevenin equivalent circuit model is used to jointly estimate the state of charge (SOC) and SOP of the lithium-ion power battery, and the variable forgetting factor recursive least squares (VFF-RLS) algorithm and extended Kalman filter (EKF) are utilized to identify the battery parameters online. Then, multiple constraint parameters including current, voltage, and SOC were derived, considering the dependence of the polarization resistance of the battery on the battery current. Finally, the verification experiment was carried out with LiFePO4 battery. The experimental results under FUDS operating conditions show that the maximum SOC estimation error is 1.94%. And the power prediction errors at 20%, 50%, and 70% SOC were 5.0%, 8.1% and 4.5%, respectively. Our further work will focus on the joint estimation of battery state to further improve the accuracy.