The state-of-charge (SOC) and state-of-health (SOH) estimation of batteries play important roles in managing batteries for automotive applications. However, an accurate state estimation of a battery is difficult to achieve because of certain factors, such as measurement noise, highly nonlinear characteristics, strong hysteresis phenomenon, and diffusion effect of batteries. In certain vehicular applications, such as idle stop-start systems (ISSs), significant errors in SOC/SOH estimation may lead to a failure in restarting a combustion engine after the shut-off period of the engine when the vehicle is at rest, such as at a traffic light. In this paper, a dual extended Kalman filter algorithm with a dynamic equivalent circuit model of a lead-acid battery is proposed to deal with this problem. The proposed algorithm adopts a battery model by taking into account the hysteresis phenomenon, diffusion effect, and parameter variations for accurate state estimations of the battery. The validity of the proposed algorithm is verified through experiments by using an absorbed glass mat valve-regulated lead-acid battery and a battery sensor cable for commercial ISS vehicles.