Calculation of total cross section for gamma gamma ->gamma Z scattering athigh energy

The total cross sections of gamma gamma --> gammaZ process for gamma gamma c. m. s. energy 91.2-2000GeV are presented. W-loop contribution is dominati ng when gamma gamma c. m. s. energy is larger than 140GeV. The total cross section has a maximum, 220 fb ( \ cos theta \ < cos15 degrees), at the gamm a gamma c. m. s. energy of 750GeV, which is larger one order of magnitude t han that in gamma gamma --> gamma gamma process. The future Photon Linear C ollider will have luminosity of the order of 10(33) Cm-2.s(-1) in which cas e more than 6000 events for gamma gamma --> gammaZ would be observable. In principle this process provides a test of the non-abelian nature of the sta ndard model, especially the anomalous triple and quartic W-boson vertices.