It is crucial to develop highly accurate forecasting techniques for electricity consumption in order to monitor and anticipate its evolution. In this work, a novel version of the discrete grey multivariate convolution model (ODGMC(1,N)) is proposed. A linear corrective term is included in the conventional GMC(1,N) structure, parameter estimation is carried out in a manner consistent with the modelling process, and an iterative technique is used to get the cumulated forecasting function of ODGMC(1,N). As a result, the forecasting capacity of ODGMC(1,N) is more reliable and its stability is enhanced. For validation purposes, ODGM(1,N) is applied to forecast Cameroon's annual electricity demand. The results show that the novel model scores 1.74% MAPE and 132.16 RMSE and is more precise than competing models.•ODGMC(1,N) corrects the linear impact ofton the forecasting performance.•Wavelet transform is used to remove irrelevant information from input data.•The proposed model can be used to track annual electricity demand.