In this paper, a novel method called online sequential extreme learning machine with under-sampling and over-sampling (OSELM-UO) for imbalanced Big data classification is proposed which combines the structures of under-sampling and over-sampling and applies online sequential extreme learning machine as its base model. The novel structure enables OSELM-UO performs well on bothminority and majority classes and simultaneously overcomes the issues of information loss and overfitting. Moreover, when the dataset keeps growing, OSELM-UO can be applied without retraining all previous data. Experiments have been conducted for OSELM-UO and several imbalance learning methods over real-world datasets respectively under high imbalance ratio (IR) and large amount of samples and features. Through the analysis of the experimental results, OSELM-UO is shown to give the best results in various aspects.