The Crystal Plasticity Finite Element Method (CPFEM) is an indispensable tool for analyzing the mechanical behavior of polycrystalline metals; however, its application is limited by the prohibitive computational costs arising from nonlinear iterative calculations with numerous internal variables. Consequently, the prohibitive computational cost remains a significant practical challenge. To address this issue, this study proposes the development of a surrogate model using the Fourier Neural Operator (FNO) for high-speed and high-accuracy prediction of three-dimensional stress fields. The primary contribution of this study lies in applying the characteristics of Operator Learning—specifically, its predictive generalization capability for unknown microstructures and its resolution independence—to crystal plasticity analysis and demonstrating their effectiveness. In this study, the FNO is trained to learn the nonlinear mapping between input fields, consisting of nodal coordinates and crystal orientations, and the output stress distributions. Specifically, we verify the generalization performance for unknown grain shapes not included in the training data and evaluate the zero-shot super-resolution capability, which enables application to grid resolutions different from those used during training without retraining. The results demonstrate that the constructed model is capable of predicting stress distributions with high accuracy, even for unknown microstructures. In particular, by applying a network trained on a computationally inexpensive coarse grid to a fine grid, the model outputs high-resolution stress fields without retraining, reproducing the tendency of local stress concentrations near grain boundaries. Furthermore, the inference time achieves a speedup of approximately 4.90 x 10^4 times compared to conventional finite element analysis. This approach realizes a balance between computational efficiency and analytical accuracy, overcoming the challenge of prohibitive computational costs and time associated with CPFEM.