Colorectal cancer is one of the highest causes of cancer-related death, especially in men. Polyps are one of the main causes of colorectal cancer, and early diagnosis of polyps by colonoscopy could result in successful treatment. Diagnosis of polyps in colonoscopy videos is a challenging task due to variations in the size and shape of polyps. In this paper, we proposed a polyp segmentation method based on the convolutional neural network. Two strategies enhance the performance of the method. First, we perform a novel image patch selection method in the training phase of the network. Second, in the test phase, we perform effective post-processing on the probability map that is produced by the network. Evaluation of the proposed method using the CVC-ColonDB database shows that our proposed method achieves more accurate results in comparison with previous colonoscopy video-segmentation methods.