In this study, the charged Higgs pair production is calculated in the context of the supersymmetry at a γγ-collider. The channel is explored in Two-parameter Non-Universal Higgs Model where the model provides relatively light neutral and charged Higgs bosons. The computation is extended to one loop-level, and the divergence arising in the loop-diagrams are cured with the radiative photon correction. The production rate of the charged Higgs pair reaches up toσ LO+NLO UU = 121 fb at √ŝ = 635 GeV. The analysis of the cross-section is also given varying the parameters mA and tan β. The total convoluted cross-section with the photon luminosity in an e + e − machine is calculated as a function of the center-of-mass energy up to 1 TeV, and it gets up to 42 fb at √ s = 900 GeV depending on the polarization of the initial electron and laser photon.