Cutting burrs, which are common in the manufacturing process of aluminum alloy wheel hubs, can severely affect the quality of the wheel hub surface and increase the scrap rate. An accurate prediction of the cutting burr size is the basis for solving the burr problem using optimization means. However, wheel hub cutting burrs can be measured only by offline microscopy, which makes acquiring burr size samples challenging, and traditional data fitting and prediction methods perform poorly for limited number of samples. To solve this problem, this paper proposes an improved method for constructing a burr length prediction model. A constitutive model of the wheel hub material A356.2 aluminum alloy is constructed using mechanical tests. This constitutive model is applied to simulate the wheel cutting burr, and the simulation results are verified using cutting experiments. Then, a large amount of simulation is performed, and a one-dimensional residual network (1D-ResNet) is constructed and trained with the simulation data; the results show that the 1D-ResNet model has stronger stability and robustness and improved prediction accuracy compared to the traditional data processing methods. Based on the transfer learning method, the trained 1D-ResNet model is fine-tuned by using the cutting experimental data, and a burr size prediction model fusing the simulation data and the experimental data is constructed. The verification results show that the proposed method can achieve high prediction accuracy with limited number of samples, thus effectively solving the engineering problem of wheel cutting burr size prediction.