Abstract: The Hexahedron Discontinuous Galerkin Time Domain algorithm requires the computational domain divided into a set of nonoverlapping curved hexahedral subdomains, each subdomain's Jacobian matrix must be obtained by map it in to a standard cube and get its mapping function. However, general commercial software can only divided computational do main into straight or low order hexahedral meshes, these meshes poorly conform to the object's boundary and bring in errors in DGTD boundary condition. This article proposed the technique of arbitrary order curved hexahedral meshes combining with Gordon-Hall method, this kind of meshes conforms with the object's boundary more accurately, and reduces the mapping function deviation obviously. Numerical results verified the technique of generating high order curved hexahedral meshes can improve the accuracy of the DGTD algorithm without increase computing resources significantly.