Cellular solids such as foam are high performance energy absorbers and are widely used in the field of automobile impact safety. Their microstructure provides the ability to undergo large plastic deformations at near constant plateau stresses, so they can absorb large amounts of kinetic energy before collapsing into a more stable structure or fracture. In order to further improve its performance, a systematic design method must be developed to adjust the behavior of microstructures by adjusting its geometric parameters, especially for microstructures with irregular and random shapes. In this work, we propose a machine learning-based method that combines finite element (FE) analysis to design open-cell foam to absorb collision energy. A large number of core points and convex polygons (called Voronoi diagrams) are used to generate foam geometry, which is then converted to a finite element model to calculate the platform stress under extrusion load. Based on the simulation data set, principal component analysis (PCA) is performed to significantly reduce the size of the design variables. Then, a linear regression function is used to establish the relationship between the structural response and the reduced design variables. The case study results show that the proposed method can effectively and efficiently design an open cell foam energy absorber with a random truss-type microstructure at a reasonable computational cost.