Robot grinding/polishing of an unknown surface requires its 3D measurement . An existing method is based on linear variable differential transformer (LVDT) that has limitations such as contact with object and low speed. In this work, a non-contact laser sensor is studied to provide faster and more accurate measurement. Measuring an unknown 3D surface of a turbine vane is challenging because some positions of the turbine vane surface are specular after being polished or grinded. In these situations, little or no measurement data are received and the reconstruction of the 3D surface profile is difficult. Here, we develop a measurement algorithm to process the laser sensor measurement data, and to reconstruct 3D profiles of these surfaces. In particular, the corrupted data due to the specular reflection are processed to obtain a nominal 3D surface profile. Three interpolation algorithms are investigated for restoring corrupted data due to specular reflection. It is found that the linear compensations of control points must be carried out before interpolation. It is necessary to obtain approximately real data of specular reflection edge by linear compensation according to true surface shape. The results of 2D profiles processed by three interpolation algorithms are displayed and compared in the same coordinates. The findings indicate that the piecewise cubic Hermite interpolation of turbine vane surface is the most promising method to restore corrupted data. The results indicate that the measurement system can meet the repairing requirement of turbine vanes .