[en] The Einstein Equivalence Principle (EEP) can be tested with deflection of light in gravitational field. In this paper, we consider the apparent shifts of active galactic nuclei (AGN) core positions are due to violations of EEP. We use data from multi-wavelength Very Long Baseline Array (VLBA) measurements and the gravitational field from our Milky Way Galaxy to put constraints on the parameterized post-Newtonian (PPN) parameter γ, and the differences of γ for photons over a frequency range of 8.11 to 15.37 GHz are within $2.30\times {10}^{-6}$, while for 1.41 to 15.37 GHz photons are within $5.75\times {10}^{-7}$, considering AGN jet properties. These results provide stringent constraints of EEP over a much wider frequency range than previous analysis.