We report the measurement of the two-photon decay width of χc2(1P) in two-photon processes at the Belle experiment. We analyze the process γγ → χc2(1P) → J/ψγ, J/ψ → ℓ+ℓ− (ℓ = e or μ) using a data sample of 971 fb−1 collected with the Belle detector at the KEKB e+e− collider. In this analysis, the product of the two-photon decay width of χc2(1P) and the branching fraction is determined to be {Gamma}_{gamma gamma}left({chi}_{c2}(1P)right)mathcal{B}left({chi}_{c2}(1P)to J/psi gamma right)mathcal{B}left(J/psi to {ell}^{+}{ell}^{-}right)=14.8pm 0.3left(textrm{stat}.right)pm 0.7left(textrm{syst}.right) eV, which corresponds to Γγγ(χc2(1P)) = 653 ± 13(stat.) ± 31(syst.) ± 17(B.R.) eV, where the third uncertainty is from mathcal{B} (χc2(1P) → J/ψγ) and mathcal{B} (J/ψ → ℓ+ℓ−).