The state of lithium-ion battery is a key indicator for the battery management system (BMS) of electric vehicles (EVs). State of charge (SOC) and state of health (SOH) of the power cell are the main parameters of the BMS during operation. In this paper, an adaptive unscented Kalman filter algorithm (AUKF) is presented for the joint estimation of SOC and SOH of lithium-ion batteries. Firstly, this paper develops a 2-RC equivalent circuit model and identifies the model parameters using recursive least squares algorithm with forgetting factor. Then, the SOC and SOH of the battery are estimated simultaneously by AUKF. Finally, the accuracy of the proposed method is verified under different operating conditions. The experiment results show that the maximum SOC estimation error is under 0.08% by the proposed method. Compared with the unscented Kalman filtering (UKF), it is shown that the proposed method is more accurate and reliable. An effective method is provided for state estimation for battery management system.