The rapid development of stealth technology has put forward the demand for lightweight, broadband and high temperature microwave absorption materials. Li_1.3Al_0.3Ti_1.7(PO₄)₃ (LATP) ceramics are selected as lightweight and high temperature microwave absorption materials, and periodic structure is designed on its surface to expand its absorption bandwidth. LATP ceramics are sintered by the high temperature solid state method. The HFSS software is used to design the periodic structure on its surface. The effects of the geometric parameters and periodic parameters of patches with different shapes on their microwave absorption properties are studied, and the genetic algorithm is adopted to optimize the periodic structure. Results show that strong electromagnetic resonance occurs near the patches of the periodic structure, effectively improving the absorption bandwidth of LATP ceramics. Compared with LATP ceramics without periodic structure, the secondary optimized rectangle ring patch can expand the absorption bandwidth with RL <−10 dB from 2.69 GHz to the entire X band. Moreover, it can increase the absorption bandwidth with RL <−15 dB from 0 GHz to 3.82 GHz. At the same time, it can also reduce the minimum reflectivity and the thickness of the ceramic.