Monthly electricity load forecasting has long been considered a challenging subject due to the variety and randomness of its impacting factors. Several academics have attempted to create numerous hybrid models combining seasonal factor with grey models. However, these studied still have limitations in determining the seasonal factor required to correctly fit seasonal data series in order to improve seasonal data forecasting. To increase prediction accuracy, the research introduces a new hybrid model that combines a fractional order accumulation grey model and seasonal factors developed using moving average (MA-SFGM(1,1)). The proposed model’s parameters are then optimised using a genetic algorithm. The new model’s reliability was confirmed by comparing it to the ARIMA and grey seasonal models using Malaysia’s monthly electricity load data from January 2011 to December 2022. The comparison findings showed that the new model performed significantly better in forecasting monthly load data.