  LB-1 was originally suggested to harbour a very massive ($ \sim 70 M_\odot $)
black hole, but was recently suggested to be a post-mass transfer binary
containing a Be star and a helium (He) star. In this paper, we use the binary
population synthesis method to simulate the potential population of the Be$ -
$He binaries in the Milky Way. Mass transfer process during the progenitor
binary evolution plays a vital role in determining the possible properties of
the Be$ - $He binary population. By constructing a range of physical models
with significantly different mass-transfer efficiencies, we obtain the
predicted distributions at the current epoch of the component masses and the
orbital periods for the Be$ - $He binaries. In particular, we show that, LB-1
very likely has evolved through non-conservative mass transfer if it is indeed
a Be$ - $He system. We estimate that there are more than $ 10^{3} $ Be$ - $He
binaries with V-band apparent magnitudes brighter than LB-1.
