Single-well productivity is a crucial metric for assessing the effectiveness of petroleum reservoir development. The accurate prediction of productivity is essential for achieving the efficient and economical development of oil–gas reservoirs. Traditional productivity prediction methods (empirical formulae and numerical simulation) are limited to specific reservoir types. There are few influencing factors, and a large number of ideal assumptions are made for the assumed conditions when predicting productivity. The application scenario is ideal. However, in tight oil reservoirs, numerous factors affect productivity, and their interactions exhibit significant complexity. Continuing to use traditional reservoir productivity prediction methods may result in significant calculation errors and lead to economic losses in oilfield development. To enhance the accuracy of tight reservoir productivity predictions and achieve economical and efficient development, this paper investigates the tight reservoir in the WZ block of the Beibuwan area, considering the impact of geological and engineering factors on productivity; the random forest tree and Spearman correlation coefficient are used to analyze the main influencing factors of productivity. The back propagation neural network optimized by particle swarm optimization was employed to develop a productivity prediction model (PSO-BP model) for offshore deep and ultra-deep tight reservoirs. The actual test well data of the oilfield are substituted into this model. The analysis results of the example application yielded an RMSE of 0.032, an MAE of 1.209, and an R2 value of 0.919. Compared with traditional productivity prediction methods, this study concludes that the model is both reasonable and practical. The calculation speed is faster and the calculation result is more accurate, which can greatly reduce productivity errors. The model constructed in this paper is well suited for predicting the productivity of tight reservoirs within the WZ block. It offers substantial guidance for predicting the productivity of similar reservoirs and supports the economical and efficient development of petroleum reservoirs.