Conical diffraction, a unique optical phenomenon in biaxial crystal, has important applications for the manipulation of particles. In this paper, a new model of annular Gaussian beam is constructed based on the Tovar's flat-topped multi-Gaussian laser beams. The conical diffraction of annular Gaussian beam is calculated using Belsky-Khapalyuk-Berry theory. The polarization characteristics of conical diffracted output beams under the annular Gaussian beam are theoretically calculated and experimentally demonstrated by means of the linearly polarized annular Gaussian beams with different polarization directions. It is found that the same azimuth angles of the inner and outer rings of the conical diffracted output beams have orthogonal polarization characteristics. A combined polarizer (CP) composed of eight polarizing segments with different specific pass axes of polarization is presented to simulate the polarization characteristic of the optical field of conical diffraction. Furthermore the calculations for output-field control of conical diffraction under the annular beam by using the proposed CP are compared with the experimental results. The results show that the intensities of both the inner and outer rings are periodically varied with CP azimuth angle. And when the azimuth angle of CP is 0, only the conical diffracted outer ring is remained, while only the inner ring of conical diffraction is remained for 180. This tunable conical diffracted field has important applications in optical tweezers and wavelength division multiplexing.