The determination of circuit type is an important prerequisite for automatic design of analog circuits. However, the same type of circuit will have some variants due to different design requirements or designers. In this paper, a graph convolution network framework used for analog circuit classification is proposed, which can effectively identify circuits and their variants. First, we convert the analog circuit netlist into the data of graph structure, and the circuit information is represented by features. By converting the data of graph structure into Fourier domain, we can convolute the circuit graph and propagate it linearly, and extract the characteristics of the circuit to identify the circuit type. We performed experiments on the data set of analog circuits, and the experimental results showed that the proposed graph convolutional network based method achieved the promising performance in identifying types of circuits and their variants.