In order to obtain a panoramic image of the inner wall of the pipeline with a large field of view, this paper uses a catadioptric panoramic optical system to achieve the panoramic imaging of the inner wall of the pipeline. However, most of the traditional catadioptric panoramic optical systems focus on the rear view, which will lead to the instability of the image distance plane of the system and the excessive pressure of the relay system. In addition, for the field of pipeline inner wall imaging, the angle between the main ray of the rear view field and the surface of the pipeline inner wall is too large, which will lead to serious information loss of the pipeline inner wall. However, the catadioptric panoramic imaging system designed in this paper pays more attention to the side view in order to obtain the information of the inner wall of the pipeline, and takes the vertical optical axis as the reference, with the pitch angle of ±25°, which is, the panoramic field of view of 360°×(65°~115°), which avoids the above problems. The mirror unit of the traditional catadioptric panoramic optical system mainly adopts even aspheric surfaces. However, due to the non orthogonality between its various coefficients, the mutual interference and even cancellation between the various coefficients, and the seriously small order of magnitude of the coefficients, the problem of low optimization efficiency of the optical system is extremely prominent. In this paper, through the study of Q-con function polynomials in three kinds of Q-type function polynomial theories, it can be seen that, compared with even aspheric surface, the base polynomials of Q-con function polynomials are orthogonal to each other, which avoids the problems of redundant interference, precision loss and numerical ill-condition caused by non-orthogonal, and provides more significant figures, improving the optimization design efficiency and machinability of an optical system. Based on the imaging principle and characteristics of the catadioptric panoramic optical system, combined with the special requirements of the panoramic imaging of the inner wall of pipeline, the relevant parameters of catadioptric panoramic optical system are formulated, and the size relationship of catadioptric panoramic optical system was analyzed. Based on the imaging characteristics, the design method of catadioptric panoramic optical system is analyzed, that is, the design method of constructing mirror unit and relay system respectively, field curvature compensation and splicing optimization. On the basis of the analysis of Q-con surface expression, this paper proposes to apply Q-con aspheric surface to the mirror element of the catadioptric panoramic optical system. The design of Q-con aspheric mirror element is analyzed, the fitting replacement and optimization method of Q-con aspheric surface of mirror element is put forward, and the catadioptric panoramic optical system based on the Q-con aspheric surface is designed. Finally, the field of view of the catadioptric panoramic optical system is (65°~115°)×360°, having a focal length of 1.24 mm, F number of 3.5, and a total length of 100 mm. The system consists of one mirror and eight lenses, in which the mirror unit adopts Q-con aspherical type, and the rest of the lenses are spherical. The Modulation Transfer Function (MTF) is greater than 0.4 at the Nyquist frequency of 93 lp/mm, and the imaging quality is close to the diffraction limit. In order to verify the advantages of Q-con surface in the design of catadioptric optical system compared with even aspheric surface, an even aspheric catadioptric panoramic system with the same parameters as Q-con aspheric catadioptric panoramic system was actually designed, and the two were analyzed and compared. The results show that compared with an even aspheric surfaces, the polynomial coefficients of Q-con aspheric surfaces are 5~17 orders of magnitude more than those of the corresponding even aspheric surfaces, which not only effectively improves the system design efficiency, processing and testing accuracy, reduces the cost, but also achieves the design results with higher image quality and smaller aperture.