The fiber geometry of communication fibers and medical fibers are always standards to evaluate the quality of optical fibers. The measurement of fiber geometry with gray scale method is one of the commonly used measurement methods. It is also the proposed method in the national standard GB15972.20-2008. In this method, the fiber geometry is obtained by fitting the elliptical curve and fitting the circular curve in two steps, but the center of the two curves may not be coincided. Thus, there is a defect in the measurement principle in the method. The measurement of fiber geometry with gray scale method has a high requirement for cutting effects and lighting conditions. When measurement conditions change, it often leads to the instability of the measured data and brings errors. In this paper, we use the arbitrary elliptical function (non-standard ellipse) which is more suitable for the fiber end face, and only use this function fitting method to get the fiber geometry to fundamentally eliminate the principle defect caused by the inconsistent center fitting between the circle fitting and the ellipse fitting. At the same time, the re-quirement of measurement condition is reduced, because the specific value of image distribution grayscale is not needed when calculating each parameter. Experiments show that this method can effectively improve the stability and consistency of measurement results.