In linear structured light measurement, in order to extract the point cloud normal vector quickly and accurately. A circumcircle extraction method is presented. Every three consecutive points are collinear or not is determined after the initial light stripe centers have been obtained by refining method. If they are collinear, the normal slope can be calculated by the points. Else, the three points determine a circle. The normal can be gotten by connecting the circle center and the initial center point. In order to reduce the shock, the average value of each three normals are calculated as the last normal. Experimental results show that the presented method can accurately extract the normal in comparison with Hessian matrix method and Sobel gradient method, and the time to process a 320 pixel × 240 pixel image is less than 8 ms, which can meet the real-time requirements.