Accurately predicting oil well production volume is of great significance in oilfield production. To overcome the shortcomings in the current study of oil well production prediction, we propose a hybrid model (GRU-KAN) with the gated recurrent unit (GRU) and Kolmogorov–Arnold network (KAN). The GRU-KAN model utilizes GRU to extract temporal features and KAN to capture complex nonlinear relationships. First, the MissForest algorithm is employed to handle anomalous data, improving data quality. The Pearson correlation coefficient is used to select the most significant features. These selected features are used as input to the GRU-KAN model to establish the oil well production prediction model. Then, the Particle Swarm Optimization (PSO) algorithm is used to enhance the predictive performance. Finally, the model is evaluated on the test set. The validity of the model was verified on two oil wells and the results on well F14 show that the proposed GRU-KAN model achieves a Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Coefficient of Determination (R2) values of 11.90, 9.18, 6.0% and 0.95, respectively. Compared to popular single and hybrid models, the GRU-KAN model achieves higher production-prediction accuracy and higher computational efficiency. The model can be applied to the formulation of oilfield-development plans, which is of great theoretical and practical significance to the advancement of oilfield technology levels.