Lattice structural materials with lightweight, multifunctional and excellent designability provide rich possibilities for intelligent materials and advanced structural design. To solve the problems of uneven stress distribution, stress concentration, and local failure, a parametric design method of functionally graded lattice structure based on stress distribution law is proposed. According to the stress distribution, the density gradient function and gradient lattice mathematical model is established, and the gradient penalty calculation of lattice cell bar size is carried out so that the relative density of cell and bar size change continuously along the height direction. The numerical simulation results show that the stress distribution of functionally graded lattice structure obtained by this method tends to be uniform under the impact load, which effectively alleviates the stress concentration effect and reduces the maximum stress by about 19%. Under the same weight reduction ratio, the material distribution is more reasonable, and the reliability and impact resistance of the structure are improved.