An estimation of the power battery state of charge (SOC) is related to the energy management, the battery cycle life and the use cost of electric vehicles. When a lithium-ion power battery is used in an electric vehicle, the SOC displays a very strong time-dependent nonlinearity under the influence of random factors, such as the working conditions and the environment. Hence, research on estimating the SOC of a power battery for an electric vehicle is of great theoretical significance and application value. In this paper, according to the dynamic response of the power battery terminal voltage during a discharging process, the second-order RC circuit is first used as the equivalent model of the power battery. Subsequently, on the basis of this model, the least squares method (LS) with a forgetting factor and the adaptive unscented Kalman filter (AUKF) algorithm are used jointly in the estimation of the power battery SOC. Simulation experiments show that the joint estimation algorithm proposed in this paper has higher precision and convergence of the initial value error than a single AUKF algorithm.