The tooth-surfaces of corrected planar double-enveloping worm wheel were established by programming in MATLAB with the theory of spatial engagement. The contact lines were analyzed, and the contact styles were classified with given parameters. A new method of judging the types of contact lines was brought out. Based on the theory of spatial engagement, the re-machined planar double-enveloping worm gear is established by programming with MATLAB software. The contact lines on the worm wheel tooth-surface are analyzed and given the method of the contact line kind judgment.