The intensity and phase of the beam propagated in the atmospheric turbulence were modulated by the effects of atmospheric turbulence, and then the speckle was formed in the far field. The partially coherent Gaussian-Schell Model (GSM) beam was taken as the research object. According to the generalized Huygens-Fresnel principle and the mode of the modified Von Karman spectrum, the expressions of the effective radius and the mean speckle radius of receiver beam were derived. The expressions were used to analyze the effects of the beam source parameters and atmospheric turbulence on the effective radius and the mean speckle radius. The numerical results show that the greater the waist radius of the beam source, the smaller the coherent length is, the smaller the wavelength is, and then the smaller the effects of atmospheric turbulence on the effective radius and the mean speckle radius of receiver beam are. The smaller refractive-index structure constant, the greater the beam spread and the smaller the mean speckle radius is. The effective radius and the mean speckle radius of receiver beam decrease with increasing inner-scale of turbulence, but have nearly no change with increasing outer-scale of turbulence. An important reference value will be provided for the design of the Acquisition, Tracking and Pointing (ATP) in atmospheric laser communication system.