  Weak Equivalent Principle (WEP) can be tested through the parameterized
post-Newtonian parameter $\gamma$, representing the space curvature produced by
unit rest mass. The parameter $\gamma$ in turn has been constrained by
comparing the arrival times of photons originating in distant transient events,
such as gamma-ray bursts, fast radio bursts as well as giant pulses of pulsars.
Those measurements normally correspond to an individual burst event with very
limited energy bands and signal-to-noise ratio (S/N). In this letter, the
discrepancy in the pulse arrival times of the Crab Pulsar between different
energy bands is obtained by the phase difference between corresponding pulse
profiles. This allows us to compare the pulse arrival times at the largest
energy band differences, between radio and optical, radio and X-ray, radio and
gamma-ray respectively. As the pulse profiles are generated by phase-folding
thousands of individual pulses, the time discrepancies between two energy bands
are actually measured from thousands of events at each energy band, which
corresponds to much higher S/N. The upper limit of the $\gamma$ discrepancy set
by such an extensively-observed and well-modeled source is as follows:
$\gamma_{radio}-\gamma_{\gamma-ray}<3.28\times10^{-9}$ at the energy difference
of $E_{\gamma-ray}/E_{radio}\sim10^{13}$,
$\gamma_{radio}-\gamma_{X-ray}<4.01\times10^{-9}$ at the energy difference of
$E_{X-ray}/E_{radio}\sim10^{9}$,
$\gamma_{radio}-\gamma_{optical}<2.63\times10^{-9}$ at
$E_{optical}/E_{radio}\sim10^{5}$, and
$\gamma_{optical}-\gamma_{\gamma-ray}<3.03\times10^{-10}$ at
$E_{\gamma-ray}/E_{optical}\sim10^8$. This actually measures the arrival times
of freely-falling photons in the gravitational field of the Milky Way with the
largest amount of events and with data of the highest S/N, which tests WEP at
the energy band differences that has never been reached before.
