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In this work, we take the $X(3872)$ as the hidden-charm tetraquark state withboth 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 takeaccount of all the Feynman diagrams, and acquire four QCD sum rules based onrigorous 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 thefirst 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 statewith the $J^{PC}=1^{++}$.

Decipher the width of the $X(3872)$ via the QCD sum rules