A critical issue in intelligent building control is detecting energy consumption anomalies based on intelligent device status data. The building field is plagued by energy consumption anomalies caused by a number of factors, many of which are associated with one another in apparent temporal relationships. For the detection of abnormalities, most traditional detection methods rely solely on a single variable of energy consumption data and its time series changes. Therefore, they are unable to examine the correlation between the multiple characteristic factors that affect energy consumption anomalies and their relationship in time. The outcomes of anomaly detection are one-sided. To address the above problems, this paper proposes an anomaly detection method based on multivariate time series. Firstly, in order to extract the correlation between different feature variables affecting energy consumption, this paper introduces a graph convolutional network to build an anomaly detection framework. Secondly, as different feature variables have different influences on each other, the framework is enhanced by a graph attention mechanism so that time series features with higher influence on energy consumption are given more attention weights, resulting in better anomaly detection of building energy consumption. Finally, the effectiveness of this paper’s method and existing methods for detecting energy consumption anomalies in smart buildings are compared using standard data sets. The experimental results show that the model has better detection accuracy.