Radiative transfer equation (RTE) is a kinetic equation modeling particles propagating through and interacting with a background medium. It has a wide range of applications including medical imaging, nuclear engineering and astrophysics. Multi-query applications, such as uncertainty quantification, inverse problem, sensitivity analysis and design optimization, require solving RTE repeatedly for various parameters, e.g. material properties. Due to its high dimensional and multiscale nature, efficient iterative solvers for RTE are highly desired. Classical diffusion synthetic acceleration (DSA) uses the diffusion limit of RTE as a preconditioner. However, when the scattering effect is not sufficiently strong, RTE may not be well-approximated by its diffusion limit. Additionally, DSA does not leverage low-rank structures of the solution manifold in the parameter-domain. To address these issues, we have developed a data-driven reduced order model (ROM) enhanced preconditioner for parametric RTE. ROM is able to exploit low-rank structures across parameters, and it also allows us to start from the original kinetic description. Intuitively, in our preconditioner, ROM corrects low frequency errors, while classical DSA damps high frequency errors. We further improve the efficiency and robustness of ROM-enhanced preconditioner by accounting for the preconditioner dependence of residual trajectory during iterations. Performance of the proposed method is demonstrated through a series of numerical tests. For some challenging 2D2V multiscale problem, our method achieves 10 times acceleration compared to classical DSA.