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A new type of toroidal worm gearing (the DTT worm drive) with concave worm profiles, ground by a grinding wheel whose two tori are symmetrical about its own mid-plane, is considered. The complete meshing theory of the DTT worm pair is established, especially including the computational method of the contact zone and the contact lines and the formulae of the induced principal curvature and the sliding angle. Furthermore, systematic researches are made on the meshing characteristics, such as the top thickness of the worm edge-tooth, the configurations of the worm helicoid and the mating wheel tooth flank and the curvature natures of the two conjugate surfaces. In addition, the effects of the technological parameters on the meshing behavior of a DTT worm set are studied in detail by means of computerized simulation approach. The obtained results demonstrate that the DTT worm pair offers advantageous meshing performance. Based on these results, the primary principles of selecting the technological parameters for processing the proposed worm set are recommended.