A new mathematical model named hollow cone double Gaussian beams is set up. Based on mathematical model of hollow double-Gaussian beams and the initial light field intensity distribution,the analytical propagation formula for hollow cone double Gaussian beams through paraxial system was derived by use of Collins formula under the cylindrical coordinates. Using the derived propagation formula,the controllable evolution properties of the intensity distribution of hollow cone double Gaussian beams in free space propagation were illustrated graphically at 1,10 and 60 m. After experenting with the biaxial crystal KNbO3,the hollow cone double Gaussian beams was obtained and the result,that the outer conic refraction angle of was equal to the convergence angle of the beams,was found. The experiment showed that the black spot areas in hollow beams increased with the transmission distance and the mathematical model of hollow cone double Gaussian beams was agreed to the experiment results basically. This research is significant for design of new laser hollow beams to generate the laser device based on hollow cone double Gaussian beams.