The current short-circuit capacity level of local area power grids is close to the rated value of the existing equipment. To address this dilemma, this paper proposes a calculation method that most closely aligns with the principles of the short-circuit capacity calculation model and the short-circuit capacity calculation method in a pure AC power system, as well as the original definitions of the short-circuit ratio and the effective short-circuit ratio index. Next, we calculate the maximum short-circuit capacity of each bus in the system using the short-circuit capacity calculation method, which is based on the current. We select the generators and active output of the loads that contribute most to the short-circuit capacity by calculating their relevant sensitivity under the typical current. We then use these generators as feature vectors to establish the training samples. Finally, we train a generalized regression neural network to calculate the short-circuit capacity in a complex grid environment. Based on this, a fast calculation model for short-circuit capacity in a complex grid environment is constructed, which can be applied to quickly scan and calculate the short-circuit capacity level of buses in an operating grid.GRNN consistently achieves the lowest MAE and RMSE values in the two datasets, B0005 and B0006. The absolute time of the calculation of several methods, namely, ICA-GPR, LS-SVR, AST-LSTM NN, and ICA-RCV, is much longer than the absolute time of GRNN. GRNN, and the absolute time of GRNN in B0006 is only 0.0077 s. It shows that the GRNN model not only optimizes the speed of calculating short-circuit capacity in complex grids but also improves the accuracy and stability of the calculation. The feasibility and effectiveness of the fast calculation model for short circuit capacity based on a generalized regression neural network have been verified.