The symmetric dark core with a high intensity ring resulting from tight focusing of an azimuthally polarized beam plays a significant role in the fields of particle trapping and high-resolution imaging, etc. However, even in the well-corrected tight focusing optical systems, some aberrations inevitably occur. Numerical calculation is performed to analyze the influence of primary aberrations on the tight focusing properties of azimuthally polarized beams based on Richards-Wolf vector diffraction theory. The results show that the primary spherical aberration and the field curvature do not destroy the circular symmetry of the intensity distribution and a sharp high intensity ring can be obtained on the real focal plane. A positional displacement of the intensity ring takes place in the presence of primary distortion. The intensity ring is elongated in the presence of primary astigmatism. The primary coma tends to drive the intensity ring to move favorably on one side of the dark core, and the intensity null vanishes when the aberration coefficient becomes large.