Transport energy demand modelling based on using a deep neural network is proposed in this paper. The energy demand prediction is based on driving cycle time series used as a model input, which is properly pre-processed and transformed into 1D or 2D static map to serve as a static input to the neural network. Several architectures of deep feedforward neural networks are considered for this application along with different formats of model inputs. Two energy demand models are derived, where the first one predicts the battery state-of-charge and fuel consumption at destination for an extended range electric vehicle, and the second one predicts the vehicle all-electric range. The models are validated based on a separate test dataset from the one used in neural network training, and they are compared with the traditional response surface approach to illustrate effectiveness of the method proposed.