Abstract: Many researches about surface approximation for cloudy measured points are reviewed. Focusing on the scattered cloudy points of free form surface with irregular boundaries, a multi-step B-spline surface approximation algorithm is presented, in which some key techniques, such as creation of boundary interpolation B-spline surface, Hardy's multiquadric local region interpolation, least square approximation of B-spline surface for regularized points, are involved. Presented algorithm is tested by an engineering experiment.