Copper-doped cadmium iodide nanocrystals were synthesized and grown for an investigation of the optical nonlinear effects via the measurements of the second harmonic generation (SHG) and nonlinear transmittance (NLT). The second-order optical susceptibilities in dependences of the size of the nanocrystals as well as of their copper contents were calculated. The observed size dependence demonstrates the nanosized quantum-confined effect, where the quantum confinement dominates the material's electronic and optical properties, with a clear increase in the SHG with decreasing the thickness of the nanocrystals. A dramatic change of the second-order optical response with increasing copper content of the nanocrystals was also observed. Optical absorption of the nanocrystals studied using NLT technique shows a decrease of the two-photon absorption with increasing thickness of the nanocrystals. The obtained results are discussed in details by exploring the photo-induced electron-phonon anharmonic mechanism for noncentrosymmetry of the impure material processes involving quantization.