In order to promote the achievement of the dual-carbon goal, this paper proposes an extended STIRPAT model and a PSO-BP neural network prediction model to analyze and predict the factors influencing carbon emissions and future carbon emissions. To address the multicollinearity problem, the STIRPAT model was validated using ridge regression, and the BP neural network was optimized using the particle swarm algorithm (PSO) to improve the prediction accuracy of the model. Taking the metal smelting industry in China as the research object, the results show that the influencing factors of carbon emission in the metal smelting industry are, in descending order, population size, energy structure, urbanization rate, intensity of energy consumption, added value of the secondary industry, and per capita GDP. In the future, the carbon emission of the metal smelting industry in China will keep the downward trend of the industry year by year, and the adjustment of the energy structure is the key to the achievement of carbon emission reduction in this industry. Finally, a series of countermeasures are proposed to reduce carbon emissions in the metal smelting industry with regard to the influencing factors and trends of carbon emissions.