  Motivated by the old idea of using the moon as a resonant gravitational-wave
(GW) detector, as well as the recent updates in modeling the lunar response to
GWs, we re-evaluate the feasibility of using a network of lunar seismometers to
constrain the stochastic GW background (SGWB). In particular, using the updated
model of the lunar response, we derive the pattern functions for the two
polarizations of GW. With these pattern functions, we further calculate the
overlap reduction functions for a network of lunar seismometers, where we have
relaxed the conventional assumption that lunar seismometers are perfectly
leveled to measure only the vertical acceleration. We apply our calculation to
two future lunar projects, namely, Chang'e and the Lunar Gravitational-Wave
Antenna (LGWA). We find that the two projects could constrain the SGWB to a
level of $\Omega_{\text{GW}}^{\text{Chang'e}} < 2.4 \times 10^{2}$ and
$\Omega_{\text{GW}}^{\text{LGWA}} < 2.0 \times 10^{-10}$, respectively, which
corresponds to a signal-to-noise ratio of SNR $=3$. These results are better
than the constraints placed previously on the SGWB in the mid-frequency band
(around $10^{-3}- 10~\text{Hz}$) by various types of experiments.
