A digital annulus is defined as a set of grid points lying between two circles sharing an identical center and separated by a given width. This paper deals with the problem of fitting a digital annulus to a given set of points in a 2D bounded grid. More precisely, we tackle the problem of finding a digital annulus that contains the largest number of inliers. As the current best algorithm for exact optimal fitting has a computational complexity in O(N 3 logN) where N is the number of grid points, we present an approximation method featuring linear time complexity and bounded error in annulus width, by extending the approximation method previously proposed for digital hyperplane fitting. Experiments show some results and runtime in practice.