Formation prediction and estimation is one of the most challenging and interesting issues in the field of networked multi-agent systems. In this paper, we propose a data-driven formation prediction algorithm to compensate for the model prediction design concept in the context of traditional multi-agent predictive control. Specifically, a novel feedback space-time graph neural network (FST-GNN) learning model is developed to predict networked multi-agent formation states with noise interference. Firstly, a state spatio-temporal dependent network graph is constructed for the physical formation of noisy multi-agent systems. Next, by introducing graph convolutional networks and gated recurrent units, the spatial structure dependencies in the multi-agent formation topology graph and the temporal dependencies of the time series data in the graph feature matrix are captured and learned, respectively. Furthermore, in order to further enhance the spatio-temporal feature extraction ability and improve prediction accuracy of our model, a feedback learning mechanism is designed by forming a closed-loop model, which can automatically improve the learning depth of the network. Finally, a series of simulation results are presented to demonstrate the effectiveness of the proposed prediction scheme.