The electricity consumption forecasting problem is especially important for policy making in developing region. To properly formulate policies, it is necessary to have reliable forecasts. Electricity consumption forecasting is influenced by some factors, such as economic, population and so on. Considering all factors is a difficult task since it requires much detailed study in which many factors significantly influence on electricity forecasting whereas too many data are unavailable. Grey convex relational analysis is used to describe the relationship between the electricity consumption and its related factors. A novel multi-variable grey forecasting model which considered the total population is developed to forecast the electricity consumption in Shandong Province. The GMC(1,N) model with fractional order accumulation is optimized by changing the order number and the effectiveness of the first pair of original data by the model is proven. The results of practical numerical examples demonstrate that the model provides remarkable prediction performances compared with the traditional grey forecasting model. The fore-casted results showed that the increase of electricity consumption will speed up in Shandong Province. (C) 2018 Elsevier Ltd. All rights reserved.