State-of-charge (SoC) and state-of-health (SoH) define the amount of charge and rated capacity loss of a battery, respectively. In order to determine these two measures, open-circuit voltage (OCV) and internal resistance of the battery are indispensable parameters that are obtained with difficulty through direct measurement. The motivation of this study is to develop an online, simple, training-free, and easily implementable scheme that is capable of estimating such parameters, particularly for the lithium-ion battery in battery-powered vehicles. Based on an equivalent circuit model (ECM), the electrical performance of a battery can be formulated into state-space representation. Also, underdetermined model parameters can be arranged to appear linearly so that an adaptive control approach can be applied. An adaptation algorithm is developed by exploiting the Lyapunov-stability criteria. The OCV and internal resistance can be extracted exactly without limitations of a system input signal, such as persistent excitation (PE), enhancing the method applicability for vehicular power systems. In this study, both simulations and experiments are established to verify the capability and effectiveness of the proposed estimation scheme.