Lung cancer is one of the most abundant causes of the cancerous deaths worldwide. It has low survival rate mainly due to the late diagnosis. With the hardware advancements in computed tomography (CT) technology, it is now possible to capture the high resolution images of lung region. However, it needs to be augmented by efficient algorithms to detect the lung cancer in the earlier stages using the acquired CT images. To this end, we propose a two-step algorithm for early detection of lung cancer. Given the CT image, we first extract the patch from the center location of the nodule and segment the lung nodule region. We propose to use Otsu method followed by morphological operations for the segmentation. This step enables accurate segmentation due to the use of data-driven threshold. Unlike other methods, we perform the segmentation without using the complete contour information of the nodule. In the second step, a deep convolutional neural network (CNN) is used for the better classification (malignant or benign) of the nodule present in the segmented patch. Accurate segmentation of even a tiny nodule followed by better classification using deep CNN enables the early detection of lung cancer. Experiments have been conducted using 6306 CT images of LIDC-IDRI database. We achieved the test accuracy of 84.13%, with the sensitivity and specificity of 91.69% and 73.16%, respectively, clearly outperforming the state-of-the-art algorithms.