Based on the principle of Hartmann-Shack wavefront sensor and the temporal and spatial analysis of the wavefront slope,a new method of measuring atmospheric parameters β ;the power-law exponent of the generalized phase power spectrum and ρ0 ;the strength of the turbulence is developed for non-Kolmogorov turbulence,by using the slope structure-correlation function and the generalized slope correlation coefficient measured by Hatmann-Shack wavefront sensor.The Hartmann-Shack wavefront sensor data acquired in recent horizontal atmospheric experiments for 1000 m laser beam propagation are used to evaluate β and ρ0 according to the method.