The ability of predicting state of a Network Slice (NS) is indispensable for the run-time management of NSs for providing proactively adjustment and reconfiguration of the NS to avoid Service Level Agreement (SLA) violation and ameliorate network resource utilization. In the literature, NS state prediction methods neglect the spatio-temporal correlation among NS entities. Moreover, NS state involves both Virtual Network Function (VNF) state and transmission link state in the virtual network of the NS. In this paper, we propose an end-to-end model by integrating Graph Neural Network (GNN) and Long Short-Term Memory (LSTM) for the dynamic NS state prediction. Typically, we apply two types of GNN models, Graph Convolutional Network (GCN) and Message Passing Neural Network (MPNN), for aggregating the spatial features for VNFs and transmission links. Then, LSTM is utilized for sequential NS state prediction. Finally, we conducted intensive simulation to validate the effectiveness of the proposed model by comparing to several baselines.