In order to illustrate the change of turbulence distance for partially coherent flat-topped (PCFT) beams propagating through non-Kolmogorov (non-K) turbulence, based on the extended Huygens-Fresnel principle and the definition of turbulence distance using relative M2-factor, the analytical expression for turbulence distance of PCFT beams through non-Kolmogorov turbulence is derived. The turbulence distance of PCFT beams through non-Kolmogorov turbulence depends on the generalized exponent parameter, inner scale and outer scale of turbulence and the initial second order moments at the plane of z=0 (namely, beam parameters including beam order, wavelength, coherence degree and beam waist width). The results show that the turbulence distance of PCFT beams through non-Kolmogorov turbulence firstly decreases towards a minimum and then increases with the increasing of generalized exponent parameter, increases with the increasing of beam order and wavelength and decreasing of coherence property, and does not monotonously vary that the turbulence distance firstly decreases and then increases with the increasing of beam waist width.