In order to reveal the potential application in aeronautic and astronautic engineering, the lattice sandwich plate subjected to in-plane compression was focused on and its mechanical behaviors were studied. Based on the failure modes including Euler buckling, shear buckling, face dimpling, face wrinkling and face crushing, a minimum mass optimization method was proposed for the lattice sandwich plate, where six optimization variables were considered, including the panel thickness, the length of rod, the size of rod cross-section, the inclined angle of rod and the wideness ratio of cell. The experimental specimens of the lattice sandwich plate were fabricated based on selective laser melting(SLM) additive manufacturing process. Then, finite element method was validated by comparison with the experimental results, and the error is less than 10%. Finally, both the initial and the optimal designs were analyzed by finite element method. Numerical results show that the optimal design can reduce 16.6% of the mass under the identical compression load, which proves the availability of the optimization method. Moreover, the consistency between the experiments and numerical result proves that additive manufacturing can be used to fabricate the lattice sandwich structure with stable mechanical properties.