Short term load forecasting is critically important in modern electricity networks since it helps provide supportive information for reliable power system operation in competitive electricity market environment. In this paper, the wavelet analysis based neural network model is employed to forecast the electricity demand in short-term period. The wavelet analysis helps to decompose the electricity demand data into different frequency bands. The Fourier transform is then employed to reveal the significant lags of these decomposed components. These lags are then used as inputs of neural network model to forecast the future values of each decomposed component. Finally, the forecasted components are combined together to form the electricity demand forecast. A case study has been reported in the paper by acquiring the data for the state of New South Wales, Australia. MAPE is used to validate the proposed model and the results show that the proposed method is promising for short term load forecasting.