In this paper, a simplified phase change model with graded porous is proposed for the problems of slow heat transfer rate and low computational efficiency in the field of latent heat storage (LHS) technology. Moreover, the proposed simplified model is further combined with the genetic algorithm to optimize the structure parameters of graded porous for the optimal strengthening effect. Considering the solidification process in the plate phase change heat storage device, the prediction accuracy and prediction efficiency of the simplified model based on the quasi-stationary approximation method are first verified. The results show that the simplified model can quickly and accurately predict the thermal performance of the LHS unit. When the effective Stefan number is less than 0.1645, the solidification time deviation is about 5% and the temperature deviation is less than 0.12%. Then, the genetic algorithm is introduced to optimize the distribution of graded porous under the different metal foam materials, metal foam consumptions, and container structure parameters. The optimization results indicate that the thermal performance of the LHS unit under different parameters gradually improves with the increase of the graded layer number. But the strengthening effect is close to the best when the graded layer number is only 4. Compared with the uniform porous structure, the solidification time can be shortened by 7.62%, while the best strengthening effect is 8.25%. Therefore, the four-graded layer structure is preferred to achieve a balance between thermal performance and structure complexity. This work can provide a simple and fast optimization design method for the structural layout of the LHS unit strengthened by graded porous.