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A new high precision and fast generation algorithm of NC tool path for triangular mesh surface was proposed, which included four steps: the first, the topological structure of the triangular mesh surface was organized by improving the R*-tree spacial index structure; the second, triangular patches were obtained based on R*-tree spacial index structure and their geometric characteristics were analyzed; the third, parabola was adopted to approximate grid borders based on the first-order continuous; the fourth, the numerical control tool path was obtained through offsetting and sorting the cutter-contact points which were calculated by intersecting between the parabola and tool section. The experimental result proves that the algorithm data have strong adaptability with high precision numerical control tool path. 