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In the paper, spatial meshing theory of involute spiroid gear drive with line contact (ISGDWLC), which is a new type of worm drive with large ratio, crossed axes and high load capacity, is presented completely for the further researches of load capacity, wear and efficiency. The methods of modeling and motion simulation are also brought forward on CATIA. Firstly, based on the spatial meshing theory, the theoretical model of ISGDWLC is proposed, including equations of flanks, meshing equation, nonundercutting conditions, conjugate zone, sliding angle and induced normal curvature. Secondly, a set of formulas for the design of ISGDWLC is provided, which has solved the problems such as undercutting, interference and redundant line of contact. In addition, in the light of simultaneous equations method the length of contact is calculated accurately, easily and rapidly. Finally, a numerical example is supplied and its sliding angle, induced normal curvature and length of contact are analyzed utilizing MATLAB. The calculations are done in a second and the analytic solutions are got. The results show that ISGDWLC not only has a simple calculation and stable instantaneous transmission ratio but also has a slight edge in local meshing performances compared to other spiroid gear drive. It has the potential to be widely used. At present, a prototype has been established according to the above work.