Radiative transfer equation (RTE) is a kinetic equation modeling particles propagating through and interacting with a background medium. Multi-query applications, such as uncertainty quantification, medical imaging, and design optimization, may require solving RTE many times for various parameters.   Classical Diffusion Synthetic Acceleration (DSA) preconditioner for RTE utilizes the diffusion limit of a kinetic correction equation. However, when the underlying scattering effect is not sufficiently strong, the correction equation may not be well approximated by its diffusion limit. DSA preconditioner may become less effective for such cases. Moreover, DSA does not exploit low-rank structures of the solution manifold with respect to parameters.   To address these issues, we utilize data-driven reduced order models (ROMs) to design a hybrid preconditioner. In the initial stage of Source Iteration or Flexible Krylov solvers, this hybrid preconditioner exploits a ROM-based low-rank approximation to the kinetic correction equation. This ROM-based low-rank approximation directly starts from the original kinetic description of the correction equation, and leverages low-rank structures across parameters. As iterations continue, we switch to classical DSA preconditioner to robustly eliminate high frequency errors. The effectiveness of the proposed method will be demonstrated through a series of numerical examples.