Convolutional neural networks (CNNs) have revolutionized medical image analysis over the past few years. The U-Net architecture is one of the most well-known CNN architectures for semantic segmentation and has achieved remarkable successes in many different medical image segmentation applications. The U-Net architecture consists of standard convolution layers, pooling layers, and upsampling layers. These convolution layers learn representative features of input images and construct segmentations based on the features. However, the features learned by standard convolution layers are not distinctive when the differences among different categories are subtle in terms of intensity, location, shape, and size. In this paper, we propose a novel CNN architecture, called Dense-Res-Inception Net (DRINet), which addresses this challenging problem. The proposed DRINet consists of three blocks, namely a convolutional block with dense connections, a deconvolutional block with residual inception modules, and an unpooling block. Our proposed architecture outperforms the U-Net in three different challenging applications, namely multi-class segmentation of cerebrospinal fluid on brain CT images, multi-organ segmentation on abdominal CT images, and multi-class brain tumor segmentation on MR images.