  Our Moon is a natural giant direct-detection target for constraining dark
matter. By considering the dark matter capture rate of the Moon, we obtain some
constraints of the spin-independent elastic scattering cross section of dark
matter particles on nucleons $\sigma_p^{\rm SI}$ using the background neutrino
data. The upper limits of $\sigma_p^{\rm SI}$ can be constrained to $\sim
10^{-38}-10^{-36}$ cm$^2$ for certain `resonance dark matter mass' ranges.
These stringent astrophysical constraints are complementary to the constraints
obtained by the direct-detection experiments.
