Reservoir productivity prediction is a key component of oil and gas field development, and the rapid and accurate evaluation of reservoir productivity plays an important role in evaluating oil field development potential and improving oil field development efficiency. Fracture-vuggy reservoirs are characterized by strong heterogeneity, complex distribution, and irregular development, causing great difficulties in the efficient prediction of fracture-vuggy reservoirs’ productivity. Therefore, a PSO-BP fracture-vuggy reservoir productivity prediction model optimized by feature optimization was proposed in this paper. The Chatterjee correlation coefficient was used to select the appropriate combination of seismic attributes as the input of the prediction model, and we applied the PSO-BP model to predict oil wells’ production in a typical fracture-vuggy reservoir area of Tahe Oilfield, China, with the selected seismic attributes and compared the accuracy with that provided by the BP neural network, linear support vector machine, and multiple linear regression. The prediction results using the four models based on the test set showed that compared with the other three models, the MSE of the PSO-BP model increased by 23% to 62%, the RMSE increased by 12 to 38 percent, the MAE increased by 18 to 44 percent, the SSE increased by 23 to 62 percent, and the R-square value increased by 2 to 13 percent. This comparison proves that the PSO-BP neural network model proposed in this paper is suitable for the productivity prediction of fracture-vuggy reservoirs and has better performance, which is of guiding significance for the development and production of fracture-vuggy reservoirs.