Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is dependent on altitude, the modified Rytov method, which is applicable to the optical wave propagation in the horizontal path, is extended to the propagation in the slant path. The formula of scintillation index as a function of the Rytov variance is derived and obtained from weak to strong fluctuation regions with Gaussian beam incidence, and the effect of the turbulence spectrum model with zero and non-zero inner scale in addition to a finite outer scale is included. The influence of different altitudes, different sizes of the inner and outer scale of the turbulence on the scintillation index with Gaussian beam propagation in the slant path is discussed in detail. Finally, the numerical results are compared and verified with the experimental data.