A neural network approach is used in the present study for modelling and estimating the energy consumption time series for a residential building in Athens, using as inputs several climatic parameters. The hourly values of the energy consumption, for heating and cooling the building, are estimated for several years using feed forward backpropagation neural networks. Various neural network architectures are designed and trained for the output estimation, which is the building's energy consumption. The results are tested with extensive sets of non-training measurements and it is found that they correspond well with the actual values. Furthermore, "multi-lag" output predictions of ambient air temperature and total solar radiation are used as inputs to the neural network models for modelling and predicting the future values of energy consumption with sufficient accuracy.