Power battery packs are the energy source of battery electric vehicles (BEVs). A precise state-of-health (SOH) estimation for batteries is crucial to ensure the operational security and stability of BEVs. This paper employs an equivalent circuit model of battery pack in SOH estimation. Since a battery pack is a complex and nonlinear system, the equivalent circuit model of battery pack is always complicated. To balance estimation accuracy and computational complexity, the equivalent circuit model of battery pack should be simplified. However, much noise is produced in the simplified model. In addition, the errors during SOH estimation are from various sources so that SOH estimation is a non-Gaussian problem. Given the genetic resampling particle filter (GPF) performs efficiently in solving non-Gaussian problems, this paper proposes a new GPF-based method for battery SOH dynamic estimation when accuracy of the equivalent circuit model is not high. First, a second-order equivalent circuit model of Resistance–Capacitance (RC) circuit for the battery pack is developed. The unknown parameters are identified using the recursive least-squares method with forgetting factor. Second, a state-space model of the GPF is developed based on the equivalent circuit model. Finally, a case study is conducted using real data collected from operating electric taxis in Beijing to investigate the estimation performance of the proposed model. Estimation results show that the proposed GPF model outperforms the particle filter method in the SOH estimation problem.