Depth information which specifies the distance between objects and current position of the robot is essential for many robot tasks such as navigation. Recently, researchers have proposed depth completion frameworks to provide dense depth maps that offer comprehensive information about the surrounding environment. However, existing methods show significant trade-offs between computational efficiency and accuracy during inference. The substantial memory and computational requirements make them unsuitable for real-time applications, highlighting the need to improve the completeness and accuracy of depth information while improving processing speed to enhance robot performance in various tasks. To address these challenges, in this paper, we propose CHADET(cross-hierarchical-attention depth-completion transformer), a lightweight depth-completion network that can generate accurate dense depth maps from RGB images and sparse depth points. For each pair, its feature is extracted from the depthwise blocks and passed to the equally lightweight transformer-based decoder. In the decoder, we utilize the novel cross-hierarchical-attention module that refines the image features from the depth information. Our approach improves the quality and reduces memory usage of the depth map prediction, as validated in both KITTI, NYUv2, and VOID datasets.