In this paper, a new high - strength worm gearing, named'rolling cone enveloping hourglass worm gearing' is proposed. With such a new type of worm gearing, the motion form between meshing tooth surfaces is changed in nature. A systematic theoretical study. a lot of numerical calculations and parameter analyses have been done. Based on these analyses,the optimum design of worm gearing is obtained. It is shown that this worm gearing possesses the virtues of high efficiency, large load capacity, long life -span and easy meanufacture.