  We investigate the resummation effects for the SM Higgs and vector boson
associated production at the LHC with a jet veto in soft-collinear effective
theory using "collinear anomalous" formalism. We calculate the jet vetoed
invariant mass distribution and the cross section for this process at
Next-to-Next-to-Leading-Logarithmic level, which are matched to the QCD
Next-to-Leading Order results, and compare the differences of the resummation
effects with different jet veto $p_{T}^{\rm veto}$ and jet radius $R$. Our
results show that both resummation enhancement effects and the scale
uncertainties decrease with the increasing of jet veto $p_{T}^{\rm veto}$ and
jet radius $R$, respectively. When $p_{T}^{\rm veto}=25$ GeV and $R=0.4~(0.5)$,
the resummation effects reduce the scale uncertainties of the Next-to-Leading
Order jet vetoed cross sections to about $7\%~(6\%)$, which lead to increased
confidence on the theoretical predictions. Besides, after including resummation
effects, the PDF uncertainties of jet vetoed cross section are about $7\%$.
