The financial market is very important to the development of social economy， so financial time series prediction （FTSP） has always been the research focus. So far， many methods based on statistical analysis and soft computing have been proposed to solve FTSP problems， most of which treat financial time series （FTS） as or convert them into stationary time series. However， since most FTSs are non-stationary， these methods usually have problems such as false regression or poor prediction performance. Therefore， this paper proposes a novel self-adaptive incremental ensemble learning （SIEL） method to solve the problem of non-stationary FTSP （NS-FTSP）. The main idea of ??the SIEL algorithm is to incrementally train a base model for each non-stationary financial time series （NS-FTS） subset， and then ensemble the base models using the adaptive weighting rule. The focus of the SIEL algorithm is the update of data weight and base model weight. The weight of data is updated based on the performance of the current ensemble model on the latest dataset， and its purpose is not to sample the data， but to weigh the error； the weight of the base model is adaptively updated based on its environment， and the performance of the base model in the newer environment should have a higher weight. In addition， in view of the characteristics of NS-FTS， the SIEL algorithm proposes a strategy to coordinate new and old knowledge and cope with the recurrence of the environment. Finally， the paper gives the experimental results of the SIEL algorithm on three NS-FTS datasets and compares them with the existing algorithms. Experimental results show that the SIEL algorithm can solve the NS-FTSP problem well.