The curved copepr mould tube is developed from the perspective of heat transfer, based on the air gap, and is analyzed by thermal deformation of the mold and shrinkage of the billet. The basic features are as follows: The copper mould tube consists of three parts viewed from the axial direction. The upper part has a varying taper in the axial direction and the lateral direction, and the lateral middle portion is convex outward; the middle portion has a varying taper in the axial direction, and the lateral direction is a square shape; the outlet portion has a varying taper in the axial direction and the lateral direction, and the lateral middle portion is concave inward to compensate for the crystallization. Thermal deformation and air gap generated by billet shrinkage, and reduce the friction of the corner portion of the outlet, so that the shell is evenly and rapidly growing in the mold, thereby obtaining high pulling speed and improving the quality of the slab.