Based on the extended Huygens-Fresnel principle, the analytical expression for the spectral degree of coherence of partially coherent annular beams propagating in atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure function, and the spatial correlation properties are studied. It is shown that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent annular beams propagate in free space, and the oscillatory behavior becomes stronger with increasing the beam obscure ratio ε. However, the oscillatory behavior becomes weaker and even disappears as the strength of turbulence increases. The curves of the spectral degree of coherence of partially coherent annular beams with different values of ε are close to each other and turn into Gaussian-like profile with increasing turbulence. The larger ε is, the less the spatial correlation is affected by the turbulence. In addition, it is found that in free space for small α the mean-squared width of the spectral degree of coherence w_c can be either larger or smaller than that of the spectral density w_i depending on ε， and critical value ε₀ increases with increasing α. As α increases, there is w_c>w_i for different values of ε. However, there always exists w_ci when the turbulence is strong enough.