This paper forecasts global mean sea level (GMSL) changes from 2024 to 2100 using weighted singular spectrum analysis (SSA) that considers the formal errors of the previous GMSL time series. The simulation experiments are first carried out to evaluate the performance of the weighted and traditional SSA approaches for GMSL change prediction with two evaluation indices, the root mean square error (RMSE) and mean absolute error (MAE). The results show that all the RMSEs and MAEs of the weighted SSA are smaller than those of the traditional SSA, indicating that the weighed SSA can predict GMSL changes more accurately than the traditional SSA. The real GMSL change rate derived from weighted SSA is approximately 1.70 ± 0.02 mm/year for 1880–2023, and the predicted GMSL changes with the first two reconstructed components reaches 796.75 ± 55.92 mm by 2100, larger than the 705.25 ± 53.73 mm predicted with traditional SSA, with respect to the baseline from 1995 to 2014. According to the sixth Assessment Report of Intergovernmental Panel on Climate Change (IPCC AR6), the GMSL change by 2100 is 830.0 ± 152.42 mm/year with the high-emission scenarios is closer to weighted SSA than traditional SSA, though SSA predictions are within the prediction range of IPCC AR6. Therefore, the weighted SSA can provide an alternative future GMSL rise prediction.