The core of this article is to study the meshing characteristics for the double circular-arc-toothed conical worm drive. So, the mathematical equation is derived for the double circular-arc-toothed conical worm, and vital results are achieved, such as, the vector equation of conical worm helicoid, the unit normal and tangent vectors, and the curvature parameters, which are deduced by the spherical vector coordinates. The relative motion coordinate system is established, some functions about the meshing of conical worm drive are derived as well. The equation of worm gear tooth surface is obtained by coordinate transformation. The tooth surface boundary equation of worm drive is derived according to the position of reference point. Finally, the performance parameters of the conical worm pair are obtained. The conjugate zones and contact lines are acquired via solving iteratively the nonlinear equation systems based on mathematics. According to the validation of numerical example of the double circular-arc-toothed conical worm drive, and the results indicate that the utilization rate of worm drive is very high and the contact stress between tooth surfaces is small.