Four-dimensional atmospheric propagation codes of high-power laser are used to simulate turbulence and thermal blooming effects of a focused solid laser beam propagating through non-Kolmogorov turbulent atmosphere. The variations of 63.2% encircled energy beam radius and beam quality factor with non-Kolmogorov turbulent spectral index α and propagation fluctuated strength D/r0 are analyzed. Deviations of simulation results of laser propagation through non-Kolmogorov turbulence and Kolmogorov turbulence are also compared. Results show that the smaller the spectral index α, the larger the beam spreading and the lower the energy concentration for turbulence effect and combined effect of turbulence and thermal blooming. The existed scaling relation for describing the beam spreading of focused Gaussian beam propagation through atmosphere is no longer valid for non-Kolmogorov turbulent atmosphere. Comparisons show that when considering the turbulence effect only, the largest relative deviation of beam spreading induced by Kolmogorov turbulence and non-Kolmogorov turbulence reaches to 87.7%, however, when considering the thermal blooming effect, the largest relative deviation reduces to 43.7%. It means that thermal blooming reduces the relative deviation of beam spreading of laser propagation in Kolmogorov and non-Kolmogorov turbulence.