  Let $k$ be an algebraically closed field of characteristic zero. We prove
that the Brauer group of moduli stack of stable parabolic
$\textnormal{PGL}(r,k)$-bundles with full flag quasi-parabolic structures at an
arbitrary parabolic divisor on a curve $X$ coincides with the Brauer group of
the smooth locus of the corresponding coarse moduli space of parabolic
$\textnormal{PGL}(r,k)$-bundles. We also compute the Brauer group of the smooth
locus of this coarse moduli for more general quasi-parabolic types and weights
satisfying certain conditions.
