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We calculate the complete next-to-leading order (NLO) QCD corrections to the$Z^0H^0$ production in association with a jet at the LHC. We study the impactsof the NLO QCD radiative corrections to the integrated and differential crosssections and the dependence of the cross section on thefactorization/renormalization scale. We present the transverse momentumdistributions of the final $Z^0$-, Higgs-boson and leading-jet. We find thatthe NLO QCD corrections significantly modify the physical observables, andobviously reduce the scale uncertainty of the LO cross section. The QCDK-factors can be 1.183 and 1.180 at the $\sqrt{s}=14 TeV$ and $\sqrt{s}=7 TeV$LHC respectively, when we adopt the inclusive event selection scheme with$p_{T,j}^{cut}=50 GeV$, $m_H=120 GeV$ and $\mu=\mu_r=\mu_f=\mu_0 \equiv1/2(m_Z+m_H)$. Furthermore, we make the comparison between the two scalechoices, $\mu=\mu_0$ and $\mu=\mu_1=1/2(E_{T}^{Z}+E_{T}^{H}+\sum_{j}E_{T}^{jet})$, and find the scale choice $\mu=\mu_1$ seems to be moreappropriate than the fixed scale $\mu=\mu_0$.

Next-to-leading order QCD predictions for $Z^0 H^0 + {\rm jet}$ production at LHC