Based on the extended Huygens-Fresnel principle and the quadratic approximation of Rytov's phase structure function, the analytical expression for the cross-spectral density function of the Gaussian Schell-Model(GSM) array beams propagating in atmospheric turbulence was derived. The degree of spatial coherence of GSM array beams in atmospheric turbulence was investigated numerically. The result shows that the spatial coherence properties of the GSM array beams are determined by the coherent length of beamlets, the transmission distance, the refractive index structure constant of atmospheric turbulence and the relative radial fill factor of the source in common. It also shows that the spatial coherence of the GSM array beams ends as Gaussian distribution, but multiple peaks are existed during the transmission, the width of the degree of coherence becomes smaller with the transmission distance continues increase which means that the degree of spatial coherence turns worse.