Most of the existing sequential learning methods for class imbalance learn data in chunks. In this paper, we propose a weighted online sequential extreme learning machine (WOS-ELM) algorithm for class imbalance learning (CIL). WOS-ELM is a general online learning method that alleviates the class imbalance problem in both chunk-by-chunk and one-by-one learning. One of the new features of WOS-ELM is that an appropriate weight setting for CIL is selected in a computationally efficient manner. In one-by-one learning of WOS-ELM, a new sample can update the classification model without waiting for a chunk to be completed. Extensive empirical evaluations on 15 imbalanced datasets show that WOS-ELM obtains comparable or better classification performance than competing methods. The computational time of WOS-ELM is also found to be lower than that of the competing CIL methods.