Monocular 3D occupancy prediction, aiming to predict the occupancy and semantics within interesting regions of 3D scenes from only 2D images, has garnered increasing attention recently for its vital role in 3D scene understanding. Predicting the 3D occupancy of large-scale outdoor scenes from 2D images is ill-posed and resource-intensive. In this paper, we present \textbf{DGOcc}, a \textbf{D}epth-aware \textbf{G}lobal query-based network for monocular 3D \textbf{Occ}upancy prediction. We first explore prior depth maps to extract depth context features that provide explicit geometric information for the occupancy network. Then, in order to fully exploit the depth context features, we propose a Global Query-based (GQ) Module. The cooperation of attention mechanisms and scale-aware operations facilitates the feature interaction between images and 3D voxels. Moreover, a Hierarchical Supervision Strategy (HSS) is designed to avoid upsampling the high-dimension 3D voxel features to full resolution, which mitigates GPU memory utilization and time cost. Extensive experiments on SemanticKITTI and SSCBench-KITTI-360 datasets demonstrate that the proposed method achieves the best performance on monocular semantic occupancy prediction while reducing GPU and time overhead.