  The accuracy of Einstein's Equivalence Principle (EEP) can be tested with the
observed time delays between correlated particles or photons that are emitted
from astronomical sources. Assuming as a lower limit that the time delays are
caused mainly by the gravitational potential of the Milky Way, we prove that
fast radio bursts (FRBs) of cosmological origin can be used to constrain the
EEP with high accuracy. Taking FRB 110220 and two possible FRB/gamma-ray burst
(GRB) association systems (FRB/GRB 101011A and FRB/GRB 100704A) as examples, we
obtain a strict upper limit on the differences of the parametrized
post-Newtonian parameter $\gamma$ values as low as $\left[\gamma(1.23\; \rm
GHz)-\gamma(1.45\; \rm GHz)\right]<4.36\times10^{-9}$. This provides the most
stringent limit up to date on the EEP through the relative differential
variations of the $\gamma$ parameter at radio energies, improving by 1 to 2
orders of magnitude the previous results at other energies based on supernova
1987A and GRBs.
