The anomalous ZZ & gamma; and Z & gamma; & gamma; neutral triple gauge couplings occurred by dimension-eight operators are investigated through the process & mu;+& mu;- & RARR; & mu;+& gamma; *& mu;- & RARR; & mu;+ Z (& nu; & nu; over bar )& mu;- at the muon collider with & RADIC;s= 3, 6, 10 and 14 TeV. The charged lepton pseudo-rapidity, the charged lepton transverse momentum and the transverse missing energy distributions are taken in consideration for the final state of the process in the analysis. The sensitivities of the anomalous couplings are obtained at 95% Confidence Level with inte-grated luminosity of Lint = 1, 4, 10 and 20 ab-1, respectively, according to center-of-mass energies of muon collider taking into account the effects of systematic uncertainties 0%, 3% and 5%. The best limits of anomalous CBB/4, CBW /4, CB W /4 and CWW /4 couplings without systematic uncertainty at center-of-mass energy of 14 TeV and integrated luminosity of 20 ab-1 are found to be [-0.01026; 0.00636] TeV-4, [-0.02482; 0.03053] TeV-4, [-0.01830; 0.02510] TeV-4, [-0.06981; 0.07387] TeV-4, respectively.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.