Accurate polyp image segmentation is of great significance, because it can help in the detection of polyps. Convolutional neural network (CNN) is a common automatic segmentation method, but its main disadvantage is the long training time. Transformer is another method that can be adapted to the automatic segmentation method by employing a self-attention mechanism, which essentially assigns different importance weights to each piece of information, thus achieving high computational efficiency during segmentation. However, a potential drawback with Transformer is the risk of information loss. The study reported in this paper employed the well-known hybridization principle to propose a method to combine CNN and Transformer to retain the strengths of both. Specifically, this study applied this method to the early detection of colonic polyps and to implement a model called MugenNet for colonic polyp image segmentation. We conducted a comprehensive experiment to compare MugenNet with other CNN models on five publicly available datasets. An ablation experiment on MugenNet was conducted as well. The experimental results showed that MugenNet can achieve a mean Dice of 0.714 on the ETIS dataset, which is the optimal performance on this dataset compared to other models, with an inference speed of 56 FPS. The overall outcome of this study is a method to optimally combine two methods of machine learning which are complementary to each other.