  Coexistence of intrinsic ferrovalley (FV) and nontrivial band topology
attracts intensive interest both for its fundamental physics and for its
potential applications, namely valley-polarized quantum anomalous Hall
insulator (VQAHI). Here, based on first-principles calculations by using
generalized gradient approximation plus $U$ (GGA+$U$) approach, the VQAHI
induced by electronic correlation or strain can occur in monolayer
$\mathrm{RuBr_2}$. For perpendicular magnetic anisotropy (PMA), the ferrovalley
(FV) to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FV
transitions can be driven by increasing electron correlation $U$. However,
there are no special QAH states and valley polarization for in-plane magnetic
anisotropy. By calculating actual magnetic anisotropy energy (MAE), the VQAHI
indeed can exist between two HVM states due to PMA, a unit Chern number/a
chiral edge state and spontaneous valley polarization. The increasing $U$ can
induce VQAHI, which can be explained by sign-reversible Berry curvature or band
inversion between $d_{xy}$/$d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Even though
the real $U$ falls outside the range, the VQAHI can be achieved by strain.
Taking $U$$=$2.25 eV as a concrete case, the monolayer $\mathrm{RuBr_2}$ can
change from a common ferromagentic (FM) semiconductor to VQAHI under about
0.985 compressive strain. It is noted that the edge states of VQAHI are
chiral-spin-valley locking, which can achieve complete spin and valley
polarizations for low-dissipation electronics devices. Both energy band gap and
valley splitting of VQAHI in monolayer $\mathrm{RuBr_2}$ are higher than the
thermal energy of room temperature (25 meV), which is key at room temperature
for device applications.
