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The successful detection of the binary neutron star (BNS) merger GW170817 andits electromagnetic (EM) counterparts has provided an opportunity to explorethe joint effect of the host galaxy and the Milky Way (MW) on the weakequivalence principle (WEP) test. In this paper, using theNavarro$-$Frenk$-$White (NFW) profile and the Herquist profile, we present ananalytic model to calculate the galactic potential, in which the possiblelocations of the source by the observed angle offset and the second supernova(SN2) kick are accounted for. We show that the upper limit of $\Delta \gamma$is $10^{-9}$ for the comparison between GW170817 and a gamma-ray burst (GRB170817A), and it is $10^{-4}$ for the comparison between GW170817 and a brightoptical transient (SSS17a, now with the IAU identification of AT 2017gfo).These limits are more stringent by one to two orders of magnitude than thosedetermined solely by the measured MW potential in the literature. Wedemonstrate that the WEP test is strengthened by contribution from the hostgalaxy to the Shapiro time delay. Meanwhile, we also find that large natalkicks produce a maximum deviation of about $20\%$ to the results with a typicalkick velocity 400$\sim$ 500 km s$^{-1}$. Finally, we analyze the impact fromthe halo mass of NGC 4993 with a typical 0.2 dex uncertainty, and find that theupper limit of $\Delta \gamma$, with a maximum mass $10^{12.4}h^{-1}M_{\odot}$, is nearly two times more stringent than that of the minimum mass$10^{12.0}h^{-1} M_{\odot}$.

Testing the weak equivalence principle with the binary neutron star merger GW170817: the gravitational contribution of the host galaxy