Current researches of incremental classification learning algorithms mainly focus on learning from data in a stationary environment. The incremental learning in a non-stationary environment (NSE), where the underlying data probability distribution changes over time, however, has received much less attentions despite the abundant real applications have generated the long-term and cumulative big data in NSE. Thus, the incremental learning in NSE has gradually received extensive attentions. Nevertheless, the popular incremental classification learning algorithms currently for NSE such as SEA and DWM generally place strict restrictions on the changes. These algorithms can only deal with gradual drift and noncyclical and no new category situations. Therefore, it is highly necessary to develop a novel efficient incremental classification learning algorithm for the gradually cumulative big data in complex NSE. The recently proposed Learn++.NSE algorithm is an important research achievement in this field. However, the vote weight of each base-classifier of the Learn++.NSE depends on its whole error rates in the environments experienced. Therefore, the classification learning efficiency of the Learn++.NSE should be further improved. A novel fast Learn++.NSE algorithm based on weighted moving average (WMA-Learn++.NSE) is presented in this paper, which computes the weighted average of error rates using the sliding window technology to optimize the weight calculation. By only using the recent classification error rates of each base-classifier inside the sliding window to calculate the vote weight, the WMA-Learn++.NSE accelerates the compute of vote weight and improves the efficiency of classification learning. The verification experiments and performance analyses on both synthetic and real data set are presented in this paper. The experimental results show that the WMA-Learn++.NSE can achieve a higher execution efficiency compared to the Learn++.NSE in getting the equivalent classification correct rate,