Supersymmetry (SUSY) is a theory which gives an explanation for the strong and electroweak interactions from the grand unification scale down to the weak scale. The search for supersymmetric particles still continues at full speed at the LHC without success. The main task at the ILC is complementing the LHC result and also search for new physics. In this study, the neutralino pair production via photon-photon collision is studied for the (tau) over tilde -coannihilation scenario in the context of MSSM at the ILC. In the calculation, all the possible one loop diagrams are taken into account for the photon-photon interaction. We present the production cross section and distribution of various observables for the lightest and next-to-lightest neutralino pairs for benchmark models which are specifically presented in the light of LHC8 data analysis, employing these benchmark models for neutralino pair production could show the potential of the ILC concerning the dark matter searches in supersymmetry.