Colorectal cancer is a common malignant tumor in the gastrointestinal tract, which usually evolves from adenomatous polyps. However, due to the similarity in color between polyps and their surrounding tissues in colonoscopy images, and their diversity in size, shape, and texture, intelligent diagnosis still remains great challenges. For this reason, we present a novel dense residual-inception network (DRI-Net) which utilizes U-Net as the backbone. Firstly, in order to increase the width of the network, a modified residual-inception block is designed to replace the traditional convolutional, thereby improving its capacity and expressiveness. Moreover, the dense connection scheme is adopted to increase the network depth so that more complex feature inputs can be fitted. Finally, an improved down-sampling module is built to reduce the loss of image feature information. For fair comparison, we validated all method on the Kvasir-SEG dataset using three popular evaluation metrics. Experimental results consistently illustrates that the values of DRI-Net on IoU, Mcc and Dice attain 77.72%, 85.94% and 86.51%, which were 1.41%, 0.66% and 0.75% higher than the suboptimal model. Similarly, through ablation studies, it also demonstrated the effectiveness of our approach in colorectal semantic segmentation.