  We propose an implementation of ZZ, ZZj and ZZjj productions in
MadGraph5_aMC@NLO framework at $\sqrt{s}$ = 14 TeV. We calculate these
processes at leading order and next-to-leading order with QCD corrections and
we present a theoretical prediction of their total cross sections with
different cuts in transverse momentum of jets, including gluon fusion
contributions. In the same time we estimate their theoretical uncertainty. We
discuss the various kinematical distributions spectrums at partonic level and
hadronic level applying the showering and hadronization using Pythia8. In order
to reconstruct the events similar to that found at LHC, we use the ATLAS cards
and the fast detector simulation Delphes.
