Predicting the remaining useful life (RUL) of lithium batteries is crucial for proactive maintenance in battery health management systems, and degradation models based on stochastic processes play an essential role. The Wiener process combined with Kalman filter method has been extensively used in this field. However, the current Wiener model has difficulty capturing the intricate aging process of lithium batteries, and online parameter estimation has low accuracy. To address these challenges, this article presents a cubic polynomial nonlinear Wiener degradation model along with a RUL adaptive prediction method, utilizing a high-order extended Kalman filter (HEKF). Firstly, a Wiener degradation model for cubic polynomials is developed by comparing the modeling accuracy of other functional models, and the incipient parameters are identified through offline stage. Then, the HEKF is designed to reduce the truncation errors by using the high order term to obtain optimal online parameter estimation. In addition, the probability density function (PDF) is established based on the definition of first hitting time (FHT) to realize adaptive prediction of RUL for lithium batteries. Finally, an example validation is carried out by the CALCE lithium battery degradation data set.