Monitoring carbon dioxide (CO₂) saturation plume movement and pressure buildup is critical for ensuring the environmental safety of geological carbon storage (GCS) projects. High-fidelity numerical simulations provide accurate modeling of CO₂ plume dynamics, but they are often computationally intensive. Recent advancements in data-driven models have enabled the rapid prediction of CO₂ plume movement. By leveraging available simulation data sets, these models offer a more efficient alternative without compromising accuracy. In this study, we adopt the U-Net enhanced graph convolutional neural network (UGCN) to predict the spatial and temporal evolution of CO₂ plume saturation and pressure buildup in saline aquifers. Utilizing the U-Net architecture, which incorporates skip connections, enables UGCN to capture high-level features and fine-grained details concurrently. We have created physics-based numerical simulation models that account for both CO₂ injection and post-injection periods. By employing the Latin-hypercube sampling method, we generated a diverse range of reservoir and decision parameters, resulting in a comprehensive simulation database. We trained and tested the UGCN model on two different data sets, including a 2D radial reservoir model (Scenario 1) and a realistic Society of Petroleum Engineers Comparative Solution Project b (SPE 11b, Scenario 2) model to train and validate the UGCN model. The performance of the UGCN model was compared with other standard graph neural networks (GNNs), such as graph convolution network (GCN) and graph attention network (GAT). Notably, the UGCN model demonstrated robust performances on the blind testing dataset, achieving an R² score of 0.993 and 0.989 for saturation predictions in Scenarios 1 and 2, respectively. Similarly, for pressure buildup the new model achieved an R² of 0.989 and 0.999 for Scenarios 1 and 2, respectively. These prediction results indicate the effectiveness of the trained models in predicting the temporal and spatial evolution of CO₂ saturation and pressure buildup predictions. Moreover, the prediction central processing unit (CPU) time for the deep learning (DL) models is significantly lower (0.02 seconds per case) than the physics-based reservoir simulator (on average, 10–15 minutes per case). This underscores the capability of the proposed method to provide predictions as accurate as physics-based simulations while reducing substantial computational costs.