A model construction scheme of chaotic optoelectronic oscillator (OEO) based on the Fourier neural operator (FNO) is proposed. Different from the conventional methods, we learn the nonlinear dynamics of OEO (actual components) in a data-driven way, expecting to obtain a multi-parameter OEO model for generating chaotic carrier with high-efficiency and low-cost. FNO is a deep learning architecture which utilizes neural network as a parameter structure to learn the trajectory of the family of equations from training data. With the assistance of FNO, the nonlinear dynamics of OEO characterized by differential delay equation can be modeled easily. In this work, the maximal Lyapunov exponent is applied to judge whether these time series have chaotic behavior, and the Pearson correlation coefficient (PCC) is introduced to evaluate the modeling performance. Compare with long and short-term memory (LSTM), FNO is not only superior to LSTM in modeling accuracy, but also requires less training data. Subsequently, we analyze the modeling performance of FNO under different feedback gains and time delays. Both numerical and experimental results show that the PCC can be greater than 0.99 in the case of low feedback gain. Next, we further analyze the influence of different system oscillation frequencies, and the generalization ability of FNO is also analyzed.