Accurate prediction of long-term electricity demand has a significant role in demand side management and electricity network planning and operation. Demand over-estimation results in over-investment in network assets, driving up the electricity prices, while demand under-estimation may lead to under-investment resulting in unreliable and insecure electricity. In this manuscript, we apply deep neural networks to predict Australia's long-term electricity demand. A stacked autoencoder is used in combination with multilayer perceptrons or cascade-forward multilayer perceptrons to predict the nation-wide electricity consumption rates for 1-24 months ahead of time. The experimental results show that the deep structures have better performance than classical neural networks, especially for 12-month to 24-month prediction horizon.