Abstract: Based on the extended Huygens-Fresnel principle, the expression for the mean-squared width of apertured polychromatic Gaussian Schell-model (GSM) beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytovs phase structure function and the method of the window function being expanded into a finite sum of complex-valued Gaussian functions. It is shown that the mean squared beam width of apertured polychromatic GSM beam increases with increasing the refractive index structure constant, the beam bandwidth and the propagation distance, and with decreasing the beam truncation parameter and the beam coherence parameter. Furthermore, apertured polychromatic GSM beams with larger bandwidth, smaller beam truncation parameter, and smaller beam coherence parameter are less affected by the turbulence. 