Single well productivity is an important index of oilfield production planning and economic evaluation. Due to fracture-vuggy reservoirs being characteristically strongly heterogeneous and having complex fluid distribution, the commonly used single well productivity prediction methods for fracture-vuggy reservoirs have many problems, such as difficulty in obtaining reservoir parameters and producing large errors in the forecast values of single well productivity. In this paper, based on the triple medium model, the Laplace transform and Duhamel principle are used to obtain the productivity equation of a single well in a fracture-vuggy reservoir. Secondly, the seismic attributes affecting the productivity of a single well are selected using the Spearman and Pearson correlation index calculation method. Finally, the selected seismic attributes are introduced into the productivity equation of the triple medium model through the interporosity flow coefficient and the elastic storativity ratio, and the undetermined coefficients under different karst backgrounds are determined using multiple nonlinear regression. From these, a new method for predicting single well productivity of fracture-vuggy reservoir is established. In order to verify the feasibility of the new method, based on the actual production data of a fracture-vuggy reservoir in Xinjiang, the new single well productivity prediction method is used to predict the productivity of 134 oil wells. The results show that the new productivity prediction method not only reduces calculation workload, but also improves the accuracy of productivity prediction, which contributes to a good foundation for future oilfield development.