Lung cancer classification in screening computed tomography (CT) scans is one of the most crucial tasks for early detection of this disease. Many lives can be saved if we are able to accurately classify malignant/cancerous lung nodules. Consequently, several deep learning based models have been proposed recently to classify lung nodules as malignant or benign. Nevertheless, the large variation in the size and heterogeneous appearance of the nodules makes this task an extremely challenging one. We propose a new Progressive Growing Channel Attentive Non-Local (ProCAN) network for lung nodule classification. The proposed method addresses this challenge from three different aspects. First, we enrich the Non-Local network by adding channel-wise attention capability to it. Second, we apply Curriculum Learning principles, whereby we first train our model on easy examples before hard ones. Third, as the classification task gets harder during the Curriculum learning, our model is progressively grown to increase its capability of handling the task at hand. We examined our proposed method on two different public datasets and compared its performance with state-of-the-art methods in the literature. The results show that the ProCAN model outperforms state-of-the-art methods and achieves an AUC of 98.05% and an accuracy of 95.28% on the LIDC-IDRI dataset. Moreover, we conducted extensive ablation studies to analyze the contribution and effects of each new component of our proposed method.