Monocular depth estimation plays a critical role in various computer vision and robotics applications such as localization, mapping, and 3D object detection. Recently, learning-based algorithms achieve huge success in depth estimation by training models with a large amount of data in a supervised manner. However, it is challenging to acquire dense ground truth depth labels for supervised training, and the unsupervised depth estimation using monocular sequences emerges as a promising alternative. Unfortunately, most studies on unsupervised depth estimation explore loss functions or occlusion masks, and there is little change in model architecture in that ConvNet-based encoder-decoder structure becomes a de-facto standard for depth estimation. In this paper, we employ a convolution-free Swin Transformer as an image feature extractor so that the network can capture both local geometric features and global semantic features for depth estimation. Also, we propose a Densely Cascaded Multi-scale Network (DCMNet) that connects every feature map directly with another from different scales via a top-down cascade pathway. This densely cascaded connectivity reinforces the interconnection between decoding layers and produces high-quality multi-scale depth outputs. The experiments on two different datasets, KITTI and Make3D, demonstrate that our proposed method outperforms existing state-of-the-art unsupervised algorithms.