Computer-aided detection systems for lung nodules play an important role in the early diagnosis and treatment process. False positive reduction is a significant component in pulmonary nodule detection. To address the visual similarities between nodules and false positives in CT images and the problem of two-class imbalanced learning, we propose a central attention convolutional neural network on imbalanced data (CACNNID) to distinguish nodules from a large number of false positive candidates. To solve the imbalanced data problem, we consider density distribution, data augmentation, noise reduction, and balanced sampling for making the network well-learned. During the network training, we design the model to pay high attention to the central information and minimize the influence of irrelevant edge information for extracting the discriminant features. The proposed model has been evaluated on the public dataset LUNA16 and achieved a mean sensitivity of 92.64%, specificity of 98.71%, accuracy of 98.69%, and AUC of 95.67%. The experimental results indicate that our model can achieve satisfactory performance in false positive reduction.