Reducing greenhouse gas (GHG) emissions has become a necessity and not an option to sustain the environment in both human and natural systems. The Slovak Republic (SR), like the European Union (EU), aims to become greenhouse gas neutral by 2050. To reach this ambitious target, emissions will need to fall by 55% compared to those in the base year 1990. Therefore, forecasting GHG emission amounts is important. The grey model is one of the widespread mathematical forecasting methods. There exist studies that have used some types of grey models to predict GHG but not in the case of the Slovak Republic. We have optimized the length of the input sequence in the rolling mechanism to enhance the forecast accuracy of a new grey model combining the Bernoulli equation with the rolling mechanism. Standard grey model, nonlinear grey Bernoulli model, and grey model with rolling mechanism were used to prove the validity of our optimization and to compare prediction performance among grey models. The novel model was also used for a long-term forecast of GHG emissions in the SR for the years from 2020 to 2040 and compared with officially reported projections. Calculated values showed that the SR is on a good way to reach set targets towards climate change mitigation.