To improve lattice sandwich panels’ anti-explosion performance, a functionally graded lattice sandwich panel structure was proposed, its upper facesheet was thinner than lower one, its upper core layer was fine and lower one was coarse (namely positive gradient distribution). The FE software ANSYS/LS-DYNA was used to study the anti-explosion performance of the new sandwich structure. Effects of facesheet gradient and core layer one on the anti-blast performance of sandwich panels were investigated, respectively. Single factor analyses were performed for size parameters of functionally graded lattice sandwich structures. The results indicated that energy absorption of lattice sandwich panels can be greatly improved by simultaneously considering positive gradient distribution of facesheet and core layer; the contribution of facesheet positive gradient distribution to energy absorption is more significant than that of core layer positive gradient distribution; moreover, the thicknesses of upper panel, lower one and core layer, and the angle between core bar and lower facesheet have a larger effect on the new structure’s anti-blast performance, while the effect of sizes of core bar’s top and bottom sections is smaller.