<p>Land-use and land-cover change (LULCC) is one of the key drivers altering terrestrial ecosystem carbon storage. Accurate simulation of LULCC is crucial for assessing ecosystem sustainability and formulating global climate change mitigation strategies. Within this context, this study proposes a novel deep learning model integrating U-Net architecture, an attention mechanism, and ConvLSTM—termed U-Net-Attention-ConvLSTM (UNA-CL), to enhance the accuracy of LULCC simulation. The model’s effectiveness was validated using land use and land cover (LULC) data from Kunming (2000–2020) and compared with a widely applied convolutional neural network (CNN) model (CNNA-CL) and Random Forest-Cellular Automata (RF-CA) model. Furthermore, this study coupled the UNA-CL model with the Integrated Valuation of Ecosystem Services and Trade-offs (InVEST) model, which is designed for ecosystem service assessment, to jointly reveal the spatiotemporal evolution characteristics of future LULC patterns and carbon storage. The results indicate that (1) the UNA-CL model outperformed the comparative models in classification accuracy, achieving an overall accuracy (OA) of 94.36%, which is 5.72% and 0.5% higher than the CNNA-CL and RF-CA models, respectively; (2) in terms of spatial allocation accuracy, the UNA-CL model not only accurately simulated land cover categories with complex distribution patterns but also mitigated the simulation bias caused by spatial heterogeneity in the RF-CA model; (3) from 2000 to 2030, the net increase in carbon storage was 3.74 Mega tons (Mt), exhibiting a trend of increase followed by decrease. Specifically, the conversion of grassland and cultivated land to forest land led to an accumulation of 3.81 Mt during 2000–2020. However, from 2020 to 2030, a combination of forest land loss and continued construction land expansion resulted in a net decrease of 0.07 Mt.</p>