  It is known that the large-scale structure (LSS) mapped by a galaxy redshift
survey is subject to distortions by galaxies' peculiar velocities. Besides the
signatures generated in common N-point statistics, such as the anisotropy in
the galaxy 2-point correlation function, the peculiar velocities also induce
distinct features in LSS's morphological properties, which are fully described
by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated
mean curvature and Euler characteristic (or genus). In this work, by using
large suite of N-body simulations, we present and analyze these important
features in the MFs of LSS on both (quasi-)linear and non-linear scales, with a
focus on the latter. We also find the MFs can give competitive constraints on
cosmological parameters compared to the power spectrum, probablly due to the
non-linear information contained. For galaxy number density similar to the DESI
BGS galaxies, the constraint on $\sigma_8$ from the MFs with one smoothing
scale can be better by $\sim 50\%$ than from the power spectrum. These findings
are important for the cosmological applications of MFs of LSS, and probablly
open up a new avenue for studying the peculiar velocity field itself.
