One of the major issues about the operation of power systems is the prediction of load demand. Moreover, load forecasting is of prime concern to system operators. Recently, the integration of power system elements, such as renewable energy sources, energy storages and electricity vehicle, brings more challenges, particularly when there are large fluctuations in forecasting cycle. This study concentrates on short-term load demand forecasting and proposes a hybrid method that combines Singular Spectrum Analysis (SSA) with deep-learning Neural Network (NN) techniques. In the beginning, the SSA technique is applied as an initial filter to remove noises. Next, a hybrid neural network, including Backpropagation Neural Network (BPNN) and Long Short-Term Memory (LSTM), is developed and trained. Then, the trained network is used as the core forecasting algorithm. Each SSA has different forms to combine with neural networks. The performance of the proposed forecasting algorithm is demonstrated using the power demand data recorded in Taiwan. Furthermore, this study compares the forecasting results by five models, including SSA, SSA-BPNN, ANN, SSA-LSTM, Wavelet Neural Network (WNN) and LSTM. The forecasting results reveal that the proposed forecasting model using Singular Spectrum Analysis provides the best performance on load forecasts.