Based on the extended Huygens-Fresnel principle and the Rytov approximate theory, analytical expressions for intensity distribution of annular beams through turbulent atmosphere have been derived. Then, according to the definition of the second-order moments of intensity, an analytical formula of M2 factor for annular beams propagating in atmospheric turbulence has been derived. Finally, the propagation properties and the changes of beam quality of annular beams through the turbulent atmosphere have been discussed in detail. The results indicate that the propagation and transformation of the annular beams through the turbulent atmosphere have been directly affected by the intensity of the turbulence. Due to the effect of the turbulence, the annular beams turn from completely coherent beams into partially coherent beams in the propagation process. The M2 factor of the annular beams depends on the obstruction ratio, the turbulence intensity, the beam wavelength and the propagation distance. By using a suitable choice of the beam parameters, such as the obstruction ratio and the wavelength of annular beams, the beam quality of annular beams in atmospheric turbulence could be effectively controlled.