  The possible non-standard interactions (NSIs) of neutrinos with matter plays
important role in the global determination of neutrino properties. In our study
we select various data sets from LHC measurements at 13 TeV with integrated
luminosities of $35 \sim 139$ fb$^{-1}$, including production of a single jet,
photon, $W/Z$ boson, or charged lepton accompanied with large missing
transverse momentum. We derive constraints on neutral-current NSIs with quarks
imposed by different data sets in a framework of either effective operators or
simplified $Z'$ models. We use theoretical predictions of productions induced
by NSIs at next-to-leading order in QCD matched with parton showering which
stabilize the theory predictions and result in more robust constraints. In a
simplified $Z'$ model we obtain a 95% CLs upper limit on the conventional NSI
strength $\epsilon$ of 0.042 and 0.0028 for a $Z'$ mass of 0.2 and 2 TeV
respectively. We also discuss possible improvements from future runs of LHC
with higher luminosities.
