  The Einstein's weak equivalence principle (WEP) is one of the foundational
assumptions of general relativity and some other gravity theories. In the
theory of parametrized post-Newtonian (PPN), the difference between the PPN
parameters $\gamma$ of different particles or the same type of particle with
different energies, $\Delta \gamma$, represents the violation of WEP. Current
constraints on $\Delta \gamma$ are derived from the observed time delay between
correlated particles of astronomical sources. However, the observed time delay
is contaminated by other effects, such as the time delays due to different
particle emission times, the potential Lorentz invariance violation and
none-zero photon rest mass. Therefore, current constraints are only upper
limits. Here we propose a new method to test WEP based on the fact that the
gravitational time delay is direction-dependent while others are not. This is
the first method which can naturally correct other time delay effects. Using
the time delay measurements of BASTE gamma-ray burst (GRB) sample and the
gravitational potential of local super galaxy cluster Laniakea, we find that
the constraint on $\Delta \gamma$ of different energy photons can be as low as
$10^{-14}$. In the future, if more gravitational wave events and fast radio
bursts with much more precise time delay measurements are observed, this method
can give a reliable and tight constraint on WEP.
