Energy is an important global issue at present, and reducing energy consumption of public organizations can promote the development of a low-carbon economy and low-carbon society, which is of immense significance to both economic and social development. In this paper, we gather dynamic energy consumption data from public institutions using the energy consumption dynamic monitoring platform, preprocess the information, and apply the 3-sigma criterion method to identify abnormal energy consumption points in these institutions. We then propose an energy consumption prediction model based on the PSO-BP neural network, use the Markov model to backtest historical energy consumption data, correct the model’s prediction results, and construct an energy consumption prediction system for public organizations. The study shows that the prediction effect of this system on energy consumption is better than that of the RS model and DS model for 1 hour and 24 hours in advance. This paper’s energy consumption prediction system effectively and timely detects and diagnoses energy consumption anomalies in public organizations’ operations, thereby supporting their energy conservation management. This paper lays the foundation for the establishment of an energy consumption prediction system and the study of energy-saving strategies. It can provide the basis and strong guidance for the optimization of energy-saving operations in public institutions.