Electricity load forecasting plays a paramount role in capacity planning, scheduling, and the operation of power systems. Reliable and accurate planning and prediction of electricity load are therefore vital. In this study, a novel approach for forecasting monthly electricity demands by wavelet transform and a neuro-fuzzy system is proposed. Firstly, the most appropriate inputs are selected and a dataset is constructed. Then, Haar wavelet transform is utilized to decompose the load data and eliminate noise. In the model, a hierarchical adaptive neuro-fuzzy inference system (HANFIS) is suggested to solve the curse-of-dimensionality problem. Several heuristic algorithms including Gravitational Search Algorithm (GSA), Cuckoo Optimization Algorithm (COA), and Cuckoo Search (CS) are utilized to optimize the clustering parameters which help form the rule base, and adaptive neuro-fuzzy inference system (ANFIS) optimize the parameters in the antecedent and consequent parts of each sub-model. The proposed approach was applied to forecast the electricity load of Hanoi, Vietnam. The constructed models have shown high forecasting performances based on the performance indices calculated. The results demonstrate the validity of the approach. The obtained results were also compared with those of several other well-known methods including autoregressive integrated moving average (ARIMA) and multiple linear regression (MLR). In our study, the wavelet CS-HANFIS model outperformed the others and provided more accurate forecasting.