This paper discusses the simultaneous state of charge (SOC) and parameter estimation of the battery for electric vehicles (EVs) and hybrid electric vehicles (HEVs). Although it is important to know the SOC and parameters of the battery to maximize its longevity, performance and reliability, there are still some difficulties in estimating them. The estimation often suffers from the battery model complexity, the poor numerical stability, and the constraints of the physical parameters of the battery. To address such issues, this paper proposes a simultaneous SOC and parameter estimation method using log-normalized UKF (LnUKF) cooperated with the battery model considering diffusion phenomena. This approach is verified by performing a series of simulations using experimental data with an EV.