The anomalous spectral behaviors of a chirped Gaussian pulsed beam diffracted by an annular aperture in the turbulent atmosphere are studied. On the basis of the extended Huygens-Fresnel principle and by introducing a hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression for the spectral intensity of chirped Gaussian pulses diffracted by an annular aperture in the turbulent atmosphere is derived. The corresponding expressions for a circular aperture, a circular black screen, and the unapertured case are given as special cases of the general results. The relative spectral shift of diffracted chirped Gaussian pulses in the turbulent atmosphere versus the different values of the radius of the annular aperture and the different values of the position parameter are also studied and illustrated with numerical calculations. The results of this work have potential applications in information encoding and transmission in a turbulent atmosphere.