We present a new approach for electricity load forecasting based on non-decimated multilevel wavelet transform, in combination with two-stage feature selection and machine learning prediction algorithm. The key idea is to decompose the non-stationary and noisy electricity load data into sub-series of different frequencies, analyse and predict them separately. The feature selection integrates autocorrelation and ranking-based methods. We evaluate the predictive performance of our approach using two years of Australian electricity data. The results show that it provides accurate predictions, outperforming exponential smoothing with single and double seasonality, the industry model and all other baselines.