The circularly orthogonal moments have been widely used in many computer vision applications. Unfortunately, they suffer from two errors namely numerical integration error and geometric error, which heavily degrade their reconstruction accuracy and pattern recognition performance. This paper describes a new kind of circularly orthogonal moments based on Chebyshev rational function. Unlike the conventional circularly orthogonal moments which have been defined in a unit disk, the proposed moment is defined in whole polar coordinates domain. In addition, given an order n, its radial projection function is smoother and oscillates at lower frequency compared with the existing circularly orthogonal moments, and so it is free of the geometric error and highly robust to the numerical integration error. Experimental results indicate that the proposed moments perform better in image reconstruction and pattern classification, and yield higher tolerance to image noise and smooth distortion in comparison with the existing circularly orthogonal moments. (C) 2016 Elsevier Inc. All rights reserved.