Recently, the development of soft sensors has shown great superiority in the measurement of unmeasurable quality variables in industrial process, which provides essential basis for the control and optimization of the process. Generally, in process with multiple quality variables, the temporal dependencies among samples and the spatial dependencies among quality variables can well reflect the inner property of a process. Therefore, the mining for spatio-temporal property will be advantageous for the promotion of soft sensor performance, while conventional methods are generally limited in learning temporal dependencies but neglect the usage for the spatial dependences among quality variables. In this paper, we propose a spatio-temporal synergistic graph convolution long short-term memory network(GC-LSTM) for the application of industrial soft sensor, which combines the spatial-mining ability of graph convolutional networks and the temporal-mining ability of long-short term memory through multi-channel network structure. The proposed model adopts spatio-temporal synergistic learning to exploit the inner property of the process, and implements soft sensing. Specifically, each quality variable is learnt independently in each channel. As for the temporal property of a process, long-short term memory networks in each channel can extract temporal features for specific quality variable. As for the spatial property of a process, a graph is constructed to describe the spatial dependencies among quality variables. Then, graph convolutional operation across channels can fuse the temporal features of different quality variables in different channels based on the spatial information in the graph for the extraction of spatio-temporal features. Thus, the proposed model implements spatio-temporal synergistic learning and fusion in the modeling process. Experiments based on the real data set from coal mill at a coal-fired power plant validate the effectiveness of the proposed model for performance improvement.