Titled pulse front pumping (TPFP) based on non-collinear phase matching is the most efficient technique to generate ultrafast terahertz (THz) wave by femtosecond laser sources, and the use of a contact grating that can avoid aberrations caused by the imaging system has the potential of further improving the generation efficiency. An embedded contact grating fabricated inside the lithium niobate crystal is proposed for the TPFP scheme for the generation of high-energy THz radiation and designed by the simplified modal method. The grating diffraction under the Littrow mounting is simplified to a two-mode interference process, which greatly simplifies the grating design. The grating period is determined and the dependence of the diffraction efficiency on the fill factor and the groove depth of the grating is systematically explored. By reducing the reflection at the grating-crystal interface the embedded grating can achieve a diffraction efficiency larger than 90% for the -1 diffraction order and the grating parameters are given. This systematic design procedure is applicable to the design of contact gratings based on other THz generation crystals.