This paper deals with the problem of controlling a series—series compensated wireless power transfer (WPT) charger for battery electric vehicle operating in constant current charging mode. The difficulty is threefold: i) The WPT charger model involves highly nonlinear terms, ii) some state variables are not accessible to measurements, and iii) the equivalent model of the battery is nonlinear; moreover, its parameters are unknown and subject to change due to several factors such as the battery state of charge (SOC), the aging and the operating temperature. To cope with all these difficulties, a nonlinear adaptive output feedback controller is designed using the backstepping control method combined with an adaptive observer-based Kalman-like and coulomb counting estimation method. The control objectives are the following: i) tight regulation of the battery charging current, ii) asymptotic stability of the closed-loop system, iii) estimation of the WPT charger’s state variables and iv) estimation of the battery internal parameters such as the SOC, the open-circuit voltage and the equivalent series resistance. The effectiveness of the proposed control strategy is highlighted by various simulation scenarios showing that all control objectives are achieved.