Abstract: Non-parallel double-roller enveloping hourglass worm gearing was proposed to eliminate the backlash. Two rows of rollers were assigned to misplacement and there was a certain defection angle between the roller axis and the radial. The working principle was introduced. According to the theories of differential geometry and space engagement theory, the static and dynamic coordinate systems of worm gear pair were established. The tooth surface equations of worm were deduced. The formulas of tooth profile of axial cross sections, tooth profile of normal cross section, meshing limit function and helix angle of the non-parallel double-roller enveloping hourglass worm gearing were derived by means of the theory of differential geometry. The parameters of R、c₂ and γ which affected the geometrical properties of the worm were analyzed. The analyzed results indicate that the tooth profile of larynx is approximately straight line, and the tooth undercutting and pointed tooth on the worm are avoided. For effectively improving the geometrical properties of the non-parallel double-roller enveloping hourglass worm gearing, R should not be more than 12 mm, c₂ should be controlled within 5 to 9 mm and γ be controlled within 18° to 25°.