The use of robots equipped with 3D laser line scanners is currently one of the mainstream geometric measurement methods for free-form surfaces. The key to this technology is to plan an effective measurement path based on the geometric features of the surface. In order to improve the measurement efficiency, a new path planning method for free-form surface measurement is proposed. First, an algorithm is developed to adaptively generate sample points of the surface to be measured based on the geodesic distance. Then, the geometric length of the scanning measurement path and the amplitude variation of the Euler angle are used as the objective function, and the optimal robot scanning measurement path is generated by minimising the objective function based on a dynamic programming algorithm. Finally, experiments show that the scanning measurement path generated based on the proposed method can effectively improve the measurement efficiency compared with existing research methods.