The horizontal propagation characteristics of supercontinuum source in non-Kolmogorov turbulence is investigated. A superposition of narrow-band spectral components is used to simulate supercontinuum. The beam width of supercontinuum source and propagation efficiency are calculated with different inner and outer scales of turbulence and parameters α, as well as with various turbulence levels and different beam qualities for the spectral parts of supercontinuum source. The method of cross-spectral density is introduced here, and the atmospheric extinction is considered. It is shown that the change of parameter α, the outer scale and inner scale of turbulence, bring about different numerical results. It is also shown that turbulence can influence the beam width and induce deterioration of propagation efficiency, especially for the situation that all the spectral parts of supercontinuum source are Gaussian fundamental modes. When the spectral parts are higher-order modes, the factor affecting propagation of supercontinuum source dominantly is diffraction.