Porous NiTi lattice structures are widely used in the manufacture of crucial components owing to their excellent shape memory effect, superelasticity, and high damping capacities. However, the specific strength and lightweight characteristics of porous NiTi lattice structures fabricated by conventional technologies are limited by unpredictability. In this work, three types of porous NiTi structures based on triply periodic minimal surface (TPMS) – Diamond, Gyroid, and Primitive – were designed and manufactured by the laser powder bed fusion (LPBF) additive manufacturing process. This work demonstrates LPBF is a feasible and efficient approach to fabricate highly accurate porous NiTi TPMS structures. Moreover, the influence of each of these structures on the mechanical and shape memory properties was investigated. Among the three structures, Gyroid had the smallest volume fraction deviation. Furthermore, the Diamond structure had the largest compressive modulus (782.82 MPa) and ultimate yield strength (163.14 MPa). The Gyroid and Primitive structures exhibit excellent elastic recovery deriving from high values of compressive modulus (662.44 MPa, and 703.29 MPa), and can maintain reliable structural robustness. The Primitive structure exhibited the lowest mechanical properties (37.80 MPa). During the cyclic compression test, Gyroid and Primitive show a smaller unrecovered strain than Diamond. Primitive shows the largest recovered strain during the heating process (6.98%). The higher mechanical flexibility of Primitive structure endows this structure with higher recovery ratio. During the direct compression test, the residual strain exhibits a positive correlation with the loading strain. All three structures exhibit good deformation recovery capability with a strain of 4%. At a strain of 12%, recovered strain during heating became the dominant factor in the recovery of the TPMS structure. Overall, porous NiTi TPMS structures are capable of reversible compressibility composed of rapid elastic recovery and controllable shape memory recovery. The unique performance of porous NiTi TPMS structure fabricated by LPBF renders it a highly efficiency energy-absorbing structure.