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Excessive energy-related carbon emission intensity will lead to deterioration of environmental quality and hinder green economic growth. This paper proposes a novel self-adaptive fractional order grey generalized Verhulst model (SAFGGVM) to predict energy-related carbon emission intensity in China, America, India, Russia, and Japan with nonlinear and complex characteristics effectively. Firstly, self-adaptive fractional order and dynamic background value coefficient are introduced to capture the nonlinear evolutionary trends. Subsequently, the optimal nonlinear parameters are determined using Grey Wolf Optimization algorithm through comprehensive comparison. Furthermore, the flexibility of SAFGGVM is verified by presenting its relevance to existing models. Finally, the validity, applicability, and robustness of SAFGGVM are confirmed by comparing with two machine learning models and four grey prediction models. The empirical results exhibit that the overall precision of SAFGGVM model significantly prevails over the others in five cases, with MAPE values less than 6% in both the simulation and prediction intervals. The out-of-sample forecast results indicate that the energy-related carbon emission intensity of five countries will fall into 5.7024, 1.6030, 7.3668, 8.1633, 2.0399 tons/10,000 USD by 2025, and the decreasing rate of developing countries tends to catch up with, or even exceed, developed countries. Projection results can serve as a reference point for countries to achieve green and sustainable development. • A novel self-adaptive grey generalized Verhulst model is proposed. • Energy-related carbon emission intensity (ECEI) of five countries is predicted. • Optimal nonlinear parameters are determined by Grey Wolf Optimization algorithm. • The novel model is superior to other competing models in accuracy and roubutness. • Decline rate of ECEI in developing countries will catch up with developed countries. [ABSTRACT FROM AUTHOR]