In this paper, a novel scheme for the condition monitoring of lithium polymer batteries is proposed, based on the sigma-point Kalman filter (SPKF) theory. For this, a runtime-based battery model is derived, from which the state-of-charge (SOC) and the capacity of the battery are accurately predicted. By considering the variation of the serial ohmic resistance ($R_o$) in this model, the estimation performance is improved. Furthermore, with the SPKF, the effects of the sensing noise and disturbance can be compensated and the estimation error due to linearization of the nonlinear battery model is decreased. The effectiveness of the proposed method is verified by Matlab/Simulink simulation and experimental results. The results have shown that in the range of a SOC that is higher than 40%, the estimation error is about 1.2% in the simulation and 1.5% in the experiment. In addition, the convergence time in the SPKF algorithm can be as fast as 300 s.