This paper introduces a novel computing method of mapping curvilinear on free formed surfaces. The method turns the sophisticated computing problem of three dimensional space into computing problem of two dimensional space with parameters

and results in improving the computing efficiency

through changing the problem of the mapping from any direction curvilinear to free formed surface into the problem of working out the intersecting points of a number of curvilinear with same parameters and general cylindrical surfaces. All of curvilinear and free formed surfaces are expressed in the same form for the utility of NURBS method

and it is advantage for the subsequent treating.