  A particular population of galaxies have drawn much interest recently, which
are as faint as typical dwarf galaxies but have the sizes as large as $L^*$
galaxies, the so called "ultra-diffuse galaxie" (UDGs). The lack of tidal
features of UDGs in dense environments suggests that their host halos are
perhaps as massive as that of the Milky Way. On the other hand, galaxy
formation efficiency should be much higher in the halos of such masses. Here we
use the model galaxy catalog generated by populating two large simulations: the
Millennium-II cosmological simulation and Phoenix simulations of 9 big clusters
with the semi-analytic galaxy formation model. This model reproduces remarkably
well the observed properties of UDGs in the nearby clusters, including the
abundance, profile, color, and morphology, etc. We search for UDG candidates
using the public data and find 2 UDG candidates in our Local Group and 23 in
our Local Volume, in excellent agreement with the model predictions. We
demonstrate that UDGs are genuine dwarf galaxies, formed in the halos of $\sim
10^{10}M_{\odot}$. It is the combination of the late formation time and
high-spins of the host halos that results in the spatially extended feature of
this particular population. The lack of tidal disruption features of UDGs in
clusters can also be explained by their late infall-time.
