The anomalous neutral triple gauge boson couplings (aNTGCs) for the Z gamma gamma and Z gamma Z vertices described by dimension-eight operators are examined through the process pp to l^{+}l^{-} gamma at the High-Luminosity Large Hadron Collider (HL-LHC). We performed an analysis on transverse momentum of photon and angular distribution of charged lepton in the final state including detector effects. Sensitivity limits of the C_{\widetilde{B}W}, C_{BB} couplings are obtained at 95 % C.L. to constrain for the range [-1.88: 1.88] TeV^{-4}, [-1.47: 1.47] TeV^{-4} and [-1.14:1.14] TeV^{-4}, [-0.86: 0.86] TeV^{-4} with an integrated luminosity of 300 fb^{-1} and 3000 fb^{-1}, respectively.
