Display omitted •A design method of nonlinear periodically gradient porous structure is proposed.•The compression failure mechanism of the nonlinear porous structure was analyzed by digital image correlation technology and finite element analysis, and a periodic failure deformation was observed.•The strain-stress plateau length and effective energy absorption were improved by increasing the number of porosity cycles. This research presents a design method of the nonlinear periodic gradient triply periodic minimal surface structures (NL-TPMS). The gradient porosity of NL-TPMS was controlled by a sinusoidal function and the influence of the number of cycles on the compression failure mechanism has been investigated. Homogenous TPMS and NL-TPMS were manufactured by laser powder bed fusion (LPBF) with 316L stainless steel powder. Digital image correlation (DIC) and finite element analysis (FEA) were applied to explore the compression behavior of NL-TPMS. The strain of the plateau end of homogenous TPMS decreases as the porosity increases, and the DIC results show that homogenous TPMS deformed with a 45° diagonal shear band. The compression results show that anisotropy of mechanical properties exists in NL-TPMS. The length of the first plateau and compressive proof strength increase as the number of cycles of porosity increases. The cycle of gradient porosity also influences the compression behavior of NL-TPMS, and a periodic failure deformation was observed in the NL-TPMS rather than a layer-by-layer compression deformation in normal gradient porous structures. The maximum principal strain of NL-TPMS detected by DIC presents a periodic distribution, which corresponds to the sinusoidal period designed function of NL-TPMS.