Lung cancer is the world's leading cause of cancer death. The convolutional neural network (CNN) has been proved able to classify between malignant and benign tissues on CT scan images. In this paper, a deep neural network is designed based on GoogleNet, a pre-trained CNN. To reduce the computing cost and avoid overfitting in network learning, the densely connected architecture of the proposed network was sparsified, with 60 % of all neurons deployed on dropout layers. The performance of the proposed network was verified through a simulation on a pre-processed CT scan image dataset: The Lung Image Database Consortium (LIDC) dataset, and compared with that of several pre-trained CNNs, namely, AlexNet, GoogleNet and ResNet50. The results show that our network achieved better classification accuracy than the contrastive networks.