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The observed time delays between photons with different circular polarizations from an astrophysical object provide a new, interesting way of testing the Einstein Equivalence Principle (EEP). In this paper, we constrain the EEP by considering both Shapiro time delay and Faraday rotation effects. We continue to search for astronomical sources that are suitable for testing the EEP accuracy, and obtain 60 extragalactic radio sources with multi-wavelength polarization angles in three different radio bands (20, 8.6, and 4.8 GHz) and 29 brightest stars within our own Milky Way galaxy with multi-colour linear polarimetric data in five optical bands ($UBVRI$). We apply the Metropolis-Hastings Markov Chain to simulate the fit parameters. The final results show that the values of the parameterized post-Newtonian parameter $γ$ discrepancy ($Δγ_{p}$) are constrained to be in the range of $10^{-26}-10^{-23}$ for 60 radio sources and in the range of $10^{-23}-10^{-20}$ for 29 optical polarization stars. Compared to previous EEP tests that based on the single polarization measurement in the gamma-ray band, our results have profound superiority that nearly a few tens of astrophysical sources with multi-wavelength polarization observations commonly in the optical and radio bands are available. It ensures that these sources can give more significantly robust bounds on the EEP. Although the presented method is straightforward, the resulting constraints on the EEP should be taken as upper limits as other more complex astrophysical effects affecting a polarization rotation are hardly considered.