Predicting network abnormal events and behavior can enhance security situation awareness and the ability to infer attack intentions. Most of the existing abnormal event prediction methods usually rely on the temporal relationship features between events and the spatial relationship features between hosts. However, the existing spatio-temporal anomaly event prediction methods do not fully consider the spatial relationship between events and the cross-domain environment of the behavior, resulting in poor performance in practical applications. In addition, the existing methods are mostly based on Euclidean space and hyperbolic space in terms of feature space relationship representation and do not fully consider the complexity of the relationship structure of anomalous events. In this paper, we propose a cross-domain spatio-temporal abnormal events prediction method, referred to as CDSTAEP. This method divides the local event sequence based on the temporal behavior sequence of entities and realizes the graphical representation of the multi-domain event correlation relationship. In the mixed-curvature space, we realize the representation learning of the correlation relationship of complex events and combine the event mixed-curvature vector representation and attention-based long short-term memory (LSTM-ATT) to capture the spatial and temporal correlation characteristics of cross-domain events, and finally realize the prediction. In this paper the proposed CDSTAEP is verified with the live network data set collected by a national key research and development plan. The results demonstrate that CDSTAEP can retain more spatial relationship features between events, the area under roc curve (AUC) score is better than the result of single-space representation and is 4.53% and 6.699% higher than the baseline models such as LSTM and LSTM-ATT.