An experiment and theoretical analysis have been done to measure the nonlinear refractive index n2 of LiNbO3 for different three wavelengths laser light of a continuous Ar-ion laser and observe the variation of the value and sign of the nonlinear refractive index. The Z-scan is a simple technique for measuring the change in phase induced on a laser beam upon propagation through a nonlinear material. It gives both the sign and magnitude of this phase change , which is simply related to the change in index of refraction, . For different wavelength the sign and the value of index of refraction is different. Additionally, for third-order nonlinear responses the real part of the third-order nonlinear susceptibility, , can be measured. However, Z- scan is sensitive to any nonlinear processes which results in , so that great care must be taken in interpreting data taken with this or any other nonlinear materials characterization technique.