Short-term load forecast is an important task in power systems. However, existing studies have overlooked the spatio-temporal adjacency between multi-sequence loads. In some cases, considering this spatio-temporal adjacency can improve the prediction accuracy. To address this problem, a fully?connected graph-based graph convolutional neural network (FCGCN) is proposed. The network first encodes the multi-sequence load data into the node feature matrix of the graph, which is combined with the method of position encoding to increase the order information of the load data. The adjacency matrix of the graph is built by using the dynamic time warping (DTW) algorithm, thus forming a fully-connected spatio-temporal graph of the load data. Then, combined with the sliding window algorithm concept, the constructed fully-connected graph is divided into a series of subgraphs, and then feature extraction is accomplished for each subgraph individually using the graph convolutional neural network (GCN). Besides, in order to realize multi-perspective feature extraction on multi-source load data, FCGCN adopts a multi-branch parallel structure. The feature vectors extracted from each branch are concatenated, and different loads are predicted through a fully-connected layer. Finally, validation experiments using actual load data from a manufacturing base show that FCGCN can achieve higher prediction accuracy compared to common prediction models.