In order to investigate the 3-D forming characteristics of multi-layer single-pass arc additive manufacture surface, the laser vision sensing system was built to collect the surface stripe images of arc additive manufacture. An region of interest (ROI) extraction method based on boundary constraints was proposed to locate the weld characteristic curve, getting the laser stripe pixel coordinates of ROI. Through theoretical analysis and experimental verification, the 3-D discrete points set of the arc additive surface were obtained, and the discrete points were fitted to form a 3-D solid surface by Delaunay triangulation algorithm. The results show that 3-D reconstruction accuracy is within 0.2mm by linear calibration method of sawtooth, and the ROI extraction method based on boundary constraints can accurately locate the stripe characteristic curve of the top surface and side surface of the arc additive manufacture. The 3-D reconstruction of the arc additive manufacture surface can visually describe the formation of the weld, which provides a new test method for surface forming inspection of arc additive manufacturing. It is beneficial for 3-D forming detection of arc additive manufacture surface.