The cost of energy consumed in educational, health, public administration, military, and other types of public buildings constitutes a substantial proportion of the total expenditure of the public sector. Due to a large number of attributes that influence the energy cost of a building, most of the models developed in the literature use only a subset of predictors, often neglect occupational data, and do not exploit enough the potential of deep learning methods. In this paper a real data from Croatian public sector is used including constructional, energetic, geographical, occupational and other attributes. Algorithms for data preprocessing and for deep learning modelling procedure are suggested. The number of hidden units in the deep neural network is optimized by a cross-validation procedure, while the sigmoid activation function was tested with Adam optimization algorithm. The feature selection was conducted using the recursive feature elimination method with a regression random forest kernel. The aims were to identify the subset of relevant predictors of energy cost in public buildings that could assist decision makers in determining the priority of reconstruction measures as well as to test the potential of deep learning in predicting the yearly energy cost. The results have shown that the deep learning network with three hidden layers was the most successful in predicting energy cost using the wrapper-based method of feature extraction. The selection of features confirms the importance of occupational data, as well as heating, cooling, electricity lightning, and constructional attributes for estimating the total energy cost. Those predictors can be used in decision making on allocating resources in public buildings reconstructions. The model implementation could improve public sector energy efficiency, save costs and contribute to the concepts of smart buildings and smart cities.