This study simultaneously considers the state-of-charge (SOC) estimation and model parameter identification of lithium-ion batteries with outliers in measurements. Conventional Kalman-type filters may degrade performance in this case since they assume Gaussian-distributed measurement noise. To improve the SOC estimation accuracy under this condition, a robust normal-gamma (NG)-based adaptive dual unscented Kalman filter (NG-ADUKF) is proposed. First, by modeling the joint distribution of the state and auxiliary variables of the measurement noise as the NG distribution, the unscented Kalman filter (UKF) is integrated with the NG filter to deal with the heavy-tailed measurement noise. Second, the online parameter identification and SOC estimation are realized simultaneously by alternatively using two NG-based adaptive UKFs. The performance of the proposed algorithm is validated by the New European Driving Cycle and Urban Dynamometer Driving Schedule tests. Experimental results show that the proposed NG-ADUKF algorithm has more accurate SOC estimations compared with the dual UKF (DUKF) and the variational Bayes-based adaptive DUKF (VB-ADUKF) in the case of mistuning and outliers. Moreover, the proposed method is more computationally efficient than VB-ADUKF.