This study presents a comprehensive modeling and analysis framework for investigating the impact of green GDP on climate factors and its potential for promoting sustainable development. Our model utilizes the entropy weight method (EWM) and grey correlation analysis (GRA) to optimize and process data, while employing a BP neural network for model training. Results indicate that green GDP leads to smaller global climate damage compared to traditional GDP, indicating its potential to alleviate the global climate crisis and promote green development.Furthermore, we built a green GDP prediction model using LSTM to forecast future changes. From the perspective of economy and management, the results indicate that transitioning from GDP to green GDP initially leads to a decrease in the index, followed by an increase. This suggests that green GDP development has short-term drawbacks but long-term benefits, including reduced resource consumption, improved economic conditions, and contribution to sustainable development. Finally, we analyzed the learning rate, number of iterations, and thresholds of related parameters through Logistic binary classification. Results demonstrate that our model is relatively stable, highlighting how green GDP addresses ecological challenges while promoting economic prosperity. These findings underscore the urgency of adopting the concept of green GDP in the contemporary era for achieving sustainable development goals.Overall, this research provides critical insights on the potential benefits and feasibility of green GDP as a crucial tool for mitigating climate risks and enhancing global prosperity.