Based on the extended Huygens-Fresnel principle, the expressions for the mean-squared width and the angular spread of apertured Gaussian Shell-model (GSM) beam propagating through atmospheric turbulent are derived by using the quadratic approximation of Rytov′s phase structure function. Compared with unapertured GSM beam, the directionality of apertured GSM beams propagating through atmospheric turbulence is studied by using angular spread and normalized far-field average intensity distribution. It is found that under a certain condition apertured GSM beams with different truncation parameter δ may have the same directionality as the corresponding unapertured GSM beam in free space and turbulence, if the angular spread in far-field is chosen as the characteristic parameter of beam directionality. On the other hand, if the beam directionality expressed in terms of the normalized far-field average intensity distribution, the directionality of different apertured GSM beams and the corresponding unapertured GSM beams in free space is not the same even if they have the same angular spreads, but the same in turbulence.