  The combination of piezoelectricity with nontrivial topological insulating
phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall
insulator (PQSHI), is intriguing for exploring novel topological states toward
the development of high-speed and dissipationless electronic devices. In this
work, we predict a PQSHI Janus monolayer VCClBr constructed from
$\mathrm{VCCl_2}$, which is dynamically, mechanically and thermally stable. In
the absence of spin orbital coupling (SOC), VCClBr is a narrow gap
semiconductor with gap value of 57 meV, which is different from Dirac semimetal
$\mathrm{VCCl_2}$. The gap of VCClBr is due to built-in electric field caused
by asymmetrical upper and lower atomic layers, which is further confirmed by
external-electric-field induced gap in $\mathrm{VCCl_2}$. When including SOC,
the gap of VCClBr is improved to 76 meV, which is larger than the thermal
energy of room temperature (25 meV). The VCClBr is a 2D topological insulator
(TI), which is confirmed by $Z_2$ topological invariant and nontrivial
one-dimensional edge states. It is proved that the nontrivial topological
properties of VCClBr are robust against strain (biaxial and uniaxial cases) and
external electric field. Due to broken horizontal mirror symmetry, only
out-of-plane piezoelectric response can be observed, when biaxial or uniaxial
in-plane strain is applied. The predicted piezoelectric strain coefficients
$d_{31}$ and $d_{32}$ are -0.425 pm/V and -0.219 pm/V, which are higher than or
compared with ones of many 2D materials. Finally, another two Janus monolayer
VCFBr and VCFCl (dynamically unstable) are constructed, and they are still
PQSHIs. Moreover, their $d_{31}$ and $d_{32}$ are higher than ones of VCClBr,
and the $d_{31}$ (absolute value) of VCFBr is larger than one.
