Abstract: Stall flutter is a single degree-of-freedom instability phenomenon that occurs due to the coupling of large pitch motion of elastic structures and dynamic stall aerodynamic forces. It is necessary to effectively predict its bifurcation speed and the limit cycle amplitude. To address the problem of predicting the aerodynamic forces during large pitch oscillations of the NACA0012 airfoil, a deep operator network (DeepONet) structure was developed, consisting of a branch net with embedded gated recurrent units or long-short-term memory neural network units and a trunk net. The DeepONet structure was trained using dynamic stall CFD aerodynamic force data for large pitch oscillations, and a high-fidelity data-driven model for dynamic stall aerodynamic forces was established, which effectively predicted unsteady aerodynamic forces for other pitch oscillations. Furthermore, the data-driven model for unsteady aerodynamic forces based on the DeepONet was coupled with the structural dynamics equation, and numerical integration was used to predict the bifurcation speed of stall flutter and the limit cycle oscillation characteristics at different speeds. The results showed that, compared with ordinary recurrent neural networks, the DeepONet could consider the hysteresis characteristics between motion and aerodynamic forces by introducing a trunk net structure, resulting in a 2% reduction in the mean absolute error in predicting aerodynamic forces during dynamic stall. Regarding the prediction of stall flutter, the error in the limit cycle oscillation amplitude was within 2%, and the DeepONet model with inflow velocity input had significantly smaller prediction errors than the operator model without velocity input.