Learning from imbalanced data sets is one of the challenging problems in machine learning, which means the number of negative examples is far more than that of positive examples. The main problems of existing methods are: (1) The degree of re-sampling, a key factor greatly affecting performance, needs to be pre-fixed, which is difficult to make the optimal choice; (2) Many useful negative samples are discarded in under-sampling; (3) The effectiveness of algorithm-level methods are limited because they just use the original training data for single classifier. To address the above issues, a novel approach of adaptive sampling with optimal cost is proposed for class-imbalance learning in this paper. The novelty of the proposed approach mainly lies in: adaptively over-sampling the minority positive examples and under-sampling the majority negative examples, forming different sub-classifiers by different subsets of training data with the best cost ratio adaptively chosen, and combining these sub-classifiers according to their accuracy to create a strong classifier. It aims to make full use of the whole training data and improve the performance of class-imbalance learning classifier. The solid experiments are conducted to compare the performance between the proposed approach and 12 state-of-the-art methods on challenging 16 UCI data sets on 3 evaluation metrics, and the results show the proposed approach can achieve superior performance in class-imbalance learning.