The analytical expression for the effective radius of curvature R of a partially coherent flat-topped beam propagating through atmospheric turbulence is derived. It is shown that R decreases due to turbulence. However, position zmin where R reaches its minimum will change due to the turbulence when the strength of turbulence is strong enough. The effective radius of curvature R increases with the increase of beam coherence parameter β when the strength of turbulence is weak, while R decreases with β increasing when the strength of turbulence is strong. The R decreases slowly with the increase of beam order M(N). The R of partially coherent flat-topped beam with larger β and smaller M(N) is more sensitive to turbulence. In addition, in free space the wavefront of partially coherent flat-topped beam can be regarded as a spherical surface in the far-field, which is independent of the beam parameters. However, in turbulence the effective radius of curvature depends on the beam parameters in the near field and also in the far field.