Offsetting of measured data, as a basic geometric operation, has already been widely used in many areas, like reverse engineering, rapid prototyping and NC machining. However, measured data always carry typical defects like caves and singular points. A fault-tolerant offset method is proposed to create the high quality offset surface of measured data with such defects. Firstly, we generated an expansion sphere model of measured data with the radius equivalent to the offset length. Secondly, using the computational geometry application of convex hull, we acquire the data of outermost enveloping surface of this expansion sphere model. Finally, we use local MLS projection fitting method to wipe out existing defects, and generate the high-quality triangular mesh surface of the offset model. The offset surface generated by this method is suitable for practical engineering application due to its high efficiency and accuracy.