Additive manufacturing technique is a promising approach for fabricating cellular bone substitutes such as trabecular and cortical bones because of the ability to adjust process parameters to fabricate different shapes and inner structures. Considering the long term safe application in human body, the metallic cellular implants are expected to exhibit superior fatigue property. The objective of the study was to study the influence of cell shape on the compressive fatigue behavior of Ti-6Al-4V mesh arrays fabricated by electron beam melting. The results indicated that the underlying fatigue mechanism for the three kinds of meshes (cubic, G7 and rhombic dodecahedron) is the interaction of cyclic ratcheting and fatigue crack growth on the struts, which is closely related to cumulative effect of buckling and bending deformation of the strut. By increasing the buckling deformation on the struts through cell shape design, the cyclic ratcheting rate of the meshes during cyclic deformation was decreased and accordingly, the compressive fatigue strength was increased. With increasing bending deformation of struts, fatigue crack growth in struts contributed more to the fatigue damage of meshes. Rough surface and pores contained in the struts significantly deteriorated the compressive fatigue strength of the struts. By optimizing the buckling and bending deformation through cell shape design, Ti-6Al-4V alloy cellular solids with high fatigue strength and low modulus can be fabricated by the EBM technique. ▪ •Ti-6Al-4V meshes with different cell shapes were fabricated by EBM technique.•The fatigue behavior of these meshes was strongly influenced by the cell shapes.•The fatigue mechanism is the interaction of cyclic ratcheting and crack growth.•Cyclic ratcheting dominated the compressive fatigue processes of these meshes.•Fatigue properties can be improved by optimizing buckling and bending deformations.