Based on the theory of non-Kolmogorov turbulence spectrum, the mathematics and physics model of laser propagation in non-Kolmogorov spectrum turbulence atmosphere is established, and numerical simulation is carried out based on the model. Results show that the turbulence spectral index has important effects on the laser propagation characteristics and its phase compensation. Under the condition of the same generalized atmospheric refractive index structure constant, the laser beam quality of far-field is better when turbulence spectral index is close to both ends of the interval (3,4). When turbulence spectral index is nearly to 4, the effect of adaptive optics compensation is better. Under the condition of the same generalized atmospheric coherence length, the peak Strehl ratio increases with the increase of turbulence spectral index. The laser propagation characteristics under normalization power spectrum are discussed, and the propagation mechanism of laser in non-Kolmogorov turbulence atmosphere is preliminary revealed.