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Extreme learning machine(ELM) is a simple and fast machine learning algorithm. However, similar to other conventional learning algorithms, the classical ELM can not well process the problem of imbalanced data distribution. In this paper, in order to improve the learning performance of classical ELM for imbalanced data learning, we present a novel variant of the ELM algorithm based on a hybrid cost function which employs the probability that given training sample belong in each class to calculate the G-mean. We perform comparable experiments for our approach and the state-of-the-arts methods on standard classification datasets which consist of 58 binary datasets and 9 multiclass datasets under different degrees of imbalance ratio. Experimental results show that our proposed algorithm can improve the classification performance significantly compared with other state-of-the-art methods.