Accurate and reliable estimation of battery state of charge (SOC) and capacity is essential for the management of the lithium-ion battery in electric vehicles. In this paper, a novel joint estimation approach of battery SOC and capacity with an adaptive variable multi-timescale framework is proposed, which also deals with the interference of current measurement offset (CMO) effectively. Aiming at the problem of unknown CMO, which will affect the accuracy of battery modeling and state estimation, an original two-stage recursive least squares algorithm is raised to identify the battery model parameters and the CMO quickly. The adaptive extended Kalman filter is applied to improve the SOC estimation accuracy by updating the noise covariance adaptively, and the recursive total least squares is used to estimate capacity with the consideration that both the battery SOC estimation and charge accumulation suffer from noises. Finally, a joint estimation of SOC and capacity structure is founded, and to address the issue of different varying characteristics of battery SOC and capacity, a novel adaptive variable multi-timescale framework is proposed. The experimental results indicate the accuracy, convergence, and adaptivity of the proposed method in different working conditions.