Inverter-based distributed power supplies are more and more widely used in new power systems, making the nonlinear characteristics of new power systems more and more significant. The low-voltage ride-through requirement exacerbates the nonlinearity, making it difficult to converge the fault analysis in distribution networks. In order to improve the convergence and accuracy of the calculation, the graph convolutional neural network algorithm is chosen in this paper to model the IIDG response current to distribution network faults under different control strategies. With the graph data processing of electrical quantities such as distribution network node voltages, fault conditions and IIDG information, the model uses graph convolution to mine the potential relationship between different features, calculate the association of features on IIDG fault response, and realize the accurate calculation of IIDG fault response output. Case study validation demonstrates that the linearized equivalent model is applicable to the fault output calculation of inverter-type distributed power supply with different control strategies under different fault types.