Based on the existing statistical data of the Lingang Special Area in Shanghai and considering its future socio-economic development, industrial structure, and technological development, a LEAP-Lingang model was developed to analyze the evolution trends of energy demand and carbon emissions under the baseline scenario, low-carbon scenario, and enhanced low-carbon scenario. To enhance the prediction accuracy of the model, the Logistic population growth model was used to predict future population data, and the learning curve model was used to simulate the cost evolution trend of related carbon reduction technologies. In addition, an economic evaluation model for carbon reduction technologies was developed, and the economic costs and emission reduction potential of typical carbon reduction technologies were evaluated by drawing a marginal emission reduction cost curve. The results showed that under the enhanced low-carbon scenario, the renewable energy accounted for 69% of the primary energy consumption, and the electric energy accounted for 91% of the terminal energy demand in 2060. The Lingang Special Area could achieve carbon peak by 2030, and the carbon emissions in 2060 were predicted to decrease by 94% compared to that in the baseline scenario. In terms of contribution to emission reduction, clean energy substitution, industrial structure optimization, and terminal energy efficiency improvement played a key role in reducing carbon emissions near the port. In the medium term (until 2035), they were predicted to contribute 35.1%, 27.3%, and 16.2% of carbon emissions, respectively, and in the long term (until 2060), they should contribute 50.6%, 8.75%, and 7.7% of carbon emissions, respectively. Regarding specific carbon reduction technologies, hydrogen power generation; water electrolysis for hydrogen; and carbon capture, utilization, and storage (CCUS) technology were of great significance for achieving net-zero emissions, but the costs of emission reduction were relatively high. The research results can provide ideas and references for the low-carbon and green development of the Lingang Special Area and related areas.