The causes of mental disorders are complex, and early recognition and early intervention are recognized as effective way to avoid irreversible brain damage over time. The existing computer-aided recognition methods mostly focus on multimodal data fusion, ignoring the asynchronous acquisition problem of multimodal data. For this reason, this paper proposes a framework of mental disorder recognition based on visibility graph (VG) to solve the problem of asynchronous data acquisition. First, time series electroencephalograms (EEG) data are mapped to spatial visibility graph. Then, an improved auto regressive model is used to accurately calculate the temporal EEG data features, and reasonably select the spatial metric features by analyzing the spatiotemporal mapping relationship. Finally, on the basis of spatiotemporal information complementarity, different contribution coefficients are assigned to each spatiotemporal feature and to explore the maximum potential of feature so as to make decisions. The results of controlled experiments show that the method in this paper can effectively improve the recognition accuracy of mental disorders. Taking Alzheimer's disease and depression as examples, the highest recognition rates are 93.73% and 90.35%, respectively. In summary, the results of this paper provide an effective computer-aided tool for rapid clinical diagnosis of mental disorders.