Accurate earthquake source-depth determination is critical for understanding tectonic processes and assessing seismic hazards. However, traditional travel-time-based location methods struggle to constrain depths due to imperfect station distribution and the strong trade-off between source depth and origin time. Deep learning holds great potential for extracting depth-related information directly from waveforms. We developed VGGDepth, a deep learning framework for earthquake depth determination. The architecture uses convolutional layers for feature extraction followed by fully connected layers that map waveform features to Gaussian-distributed depth predictions. We implemented two approaches: (1) a single-station model using three-component waveforms, validated on the 2016-2017 Central Apennines, Italy, and (2) a regional multi-station model for Southern California, processing four-channel inputs from multiple stations (three-component waveforms plus epicentral distance). The multi-station model, trained on over 300,000 earthquakes (2010-2024) with 10+ million samples, achieves mean absolute errors within 0.3 km across the 0-25 km depth range with a >99% recall rate. Both approaches demonstrate strong performance and generalizability, offering fast and accurate depth relocation capabilities for real-time applications and historical earthquake reassessment.