With the development of robotics and vision measurement technology, the use of robots with line laser scanners for 3D scanning and measurement of parts has become a mainstream trend in the field of industrial inspection. Traditional scanning and measuring robots mainly use the teach-in scanning method, which has unstable scanning quality and low scanning efficiency. In this paper, the adaptive sampling method for a free-form surface, which can realize the adaptive distribution of surface measurement points according to the curvature features of free-form surfaces, is proposed first. Then, integrated with the proposed adaptive sampling method, the automatic path planning method is proposed. This method consists of adaptive sampling, scanning attitude calculation based on a quaternion, scanning viewpoint planning based on viewable cones, and scan path generation based on bi-directional scanning. Based on the proposed automatic path planning method, the scanning and measuring robot can obtain complete 3D information of the surface to be measured with high measurement accuracy and efficiency. The performance index of the laser scanner can be fully reached.