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Ensemble models achieve high accuracy by combining a number of base estimators and can increase the reliability of machine learning compared to a single estimator. Additionally, an ensemble model enables a machine learning method to deal with imbalanced data, which is considered to be one of the most challenging problems in machine learning. In this paper, the capability of Adaptive Boosting (AdaBoost) is integrated with a Convolutional Neural Network (CNN) to design a new machine learning method, AdaBoost-CNN, which can deal with large imbalanced datasets with high accuracy. AdaBoost is an ensemble method where a sequence of classifiers is trained. In AdaBoost, each training sample is assigned a weight, and a higher weight is set for a training sample that has not been trained by the previous classifier. The proposed AdaBoost-CNN is designed to reduce the computational cost of the classical AdaBoost when dealing with large sets of training data, through reducing the required number of learning epochs for its ingredient estimator. AdaBoost-CNN applies transfer learning to sequentially transfer the trained knowledge of a CNN estimator to the next CNN estimator, while updating the weights of the samples in the training set to improve accuracy and to reduce training time. Experimental results revealed that the proposed AdaBoost-CNN achieved 16.98% higher accuracy compared to the classical AdaBoost method on a synthetic imbalanced dataset. Additionally, AdaBoost-CNN reached an accuracy of 94.08% on 10,000 testing samples of the synthetic imbalanced dataset, which is higher than the accuracy of the baseline CNN method, i.e. 92.05%. AdaBoost-CNN is computationally efficient, as evidenced by the fact that the training simulation time of the proposed method is 47.33 seconds, which is lower than the training simulation time required for a similar AdaBoost method without transfer learning, i.e. 225.83 seconds on the imbalanced dataset. Moreover, when compared to the baseline CNN, AdaBoost-CNN achieved higher accuracy when applied to five other benchmark datasets including CIFAR-10 and Fashion-MNIST. AdaBoost-CNN was also applied to the EMNIST datasets, to determine its impact on large imbalanced classes, and the results demonstrate the superiority of the proposed method compared to CNN.