The mathematical model of globoidal worm drive with high-order modification is established system? atically. The curvature parameters，meshing function and curvature interference boundary function of worm pair are derived by differential geometry and meshing theory. It is proved that the tooth surface of globoidal worm is an unde? velopable ruled surface，which is consistent with the principle of tooth surface formation. The least squares method is used to fit the dimensionless modification data to obtain a universal high-order modification curve. Based on the curve，the calculation formula of the process transmission ratio is derived，and the high-order modification worm transmission is obtained. According to the numerical examples of different modification curves，the analysis shows that the high-order modification can eliminate the constant contact line of the tooth surface of the original globoidal worm，and effectively increase the conjugate area of the tooth surface of the worm pair. After the modification，the full length of the worm can be used and the bearing capacity is strong. However，there is a curvature interference line on the tooth surface of the worm pair after high-order modification，which may lead to undercutting of the worm pair.