Gauge boson self-couplings are completely defined by the non-abelian gauge symmetry of the Standard Model (SM), thus direct search for these couplings are extremely significant in understanding the gauge structure of the SM. However, the possible deviation from the SM predictions of gauge boson self-couplings would be a sign of the presence of new physics beyond the SM. In this work, we study the sensitivities on the anomalous couplings defined by dimension-8 operators related to the ZZγγ and Zγγγ quartic vertices through the process e + e − → Zγγ with Z-boson decaying to charged leptons at the Compact Linear Collider(CLIC). We analyze the center-ofmass energy of 3 TeV, integrated luminosities of L = 1, 4, 5 ab −1 , systematic uncertainties of δ sys = 0%, 5%, 10%, and unpolarized and polarized electron beams for extraction of expected sensitivity on the anomalous f T,j /Λ 4 couplings at 95% confidence level, which are especially sensitive to the Zγγ channel. It is clear from the results that if the systematic error is improved, we expect better limits on the couplings. However, the best limits obtained on the anomalous quartic couplings for the process e + e − → Zγγ with √ s = 3 TeV, L = 5 ab −1 and δ sys = 0% can be approximately improved up to about two times better than the limits obtained with δ sys = 10%.Our sensitivities on the anomalous quartic couplings with δ sys = 0% can set more stringent sensitivity by two orders of magnitude with respect to the best sensitivity derived from the current experimental limits. Finally, with initial electron beam polarization, the sensitivity of anomalous quadratic couplings improves by almost a factor of 1.2.