The least-square method is usually adopted for fitting of geometric elements in a coordinate measurement. However, in the process of short arc measurement, it is difficult to offer a high precision due to the lack of feature points and the influence of noise jamming. Aimed at the measurement of short arc,this paper analyzes the influence of central angles on measurement errors of circle centre and radius by using the least-square method. Based on the fact that the circle center of the short arc is often set in a fixed position due to its functional property and processing technology,a centre constraint least-square circle fitting method is proposed in the study. It is proved that the measurement error is less than 0.01 mm by using the proposed method to measure a short arc with a central angle of 20° and a radius of 10 mm. A comparative experiment shows that the centre constraint least-square method can improve the accuracy of circle fitting efficiently in the short arc measurement. As the proposed method is based on machine vision system, it has advantages of high accuracy, fast speed, wide measuring ranges and on-line and non-contact measurement as compared with traditional measurement methods of short arc.