  In this work, we take the $X(3872)$ as the hidden-charm tetraquark state with
both isospin $I=0$ and $1$ components, then investigate the strong decays
$X(3872)\to J/\psi \pi^+\pi^-$, $J/\psi\omega$, $\chi_{c1}\pi^0$,
$D^{*0}\bar{D}^0$ and $D^{0}\bar{D}^0\pi^0$ with the QCD sum rules. We take
account of all the Feynman diagrams, and acquire four QCD sum rules based on
rigorous quark-hadron duality. We obtain the total decay width about
$1\,\rm{MeV}$, which is in excellent agreement with the experiment data $
\Gamma_{X}=1.19\pm 0.21\,\rm{MeV}$ from the Particle Data Group, it is the
first time to reproduce the tiny width of the $X(3872)$ via the QCD sum rules,
which supports assigning the $X(3872)$ as the hidden-charm tetraquark state
with the $J^{PC}=1^{++}$.
