In this paper, a novel learning method called Post- Boosting using extended G-mean (PBG) is proposed for online sequential multi-class imbalance learning (OS-MIL) in neural networks. PBG is effective due to three reasons: i) Through post-adjusting a classification boundary under extended G-mean, the challenging issue of imbalanced class distribution (ICD) for sequentially arriving multi-class data can be effectively resolved. ii) A newly derived update rule for online sequential learning is proposed, which produces a high G-mean for current model and simultaneously possesses almost the same information of its previous models. iii) A dynamic adjustment mechanism provided by extended G-mean is valid to deal with the unresolved challenging dense-majority problem and two dynamic changing issues, namely, dynamic changing data scarcity (DCDS) and dynamic changing data diversity (DCDD). Compared to other OS-MIL methods, PBG is highly effective on resolving DCDS, while PBG is the only method to resolve dense-majority and DCDD. Furthermore, PBG can directly and effectively handle unscaled data stream. Experiments have been conducted for PBG and two popular OS-MIL methods for neural networks under massive binary and multi-class datasets. Through the analyses of experimental results, PBG is shown to outperform the other compared methods on all datasets in various aspects including the issues of data scarcity, dense-majority, DCDS, DCDD, and unscaled data.