TPMS (Triply periodic minimal surface) has attracted significant attention recently because of its superior energy-absorbing properties. To improve its energy-absorbing performance and designability, a heteromorphic structure for TPMS is proposed. This structure is formed by the fusion of two kinds of TPMS and inherits the structural characteristics of both TPMS. We systematically investigate Heteromorphic TPMS and Multi-morphology TPMS using quasi-static compression tests and finite element simulations. The results showed that the Heteromorphic TPMS with Gyroid and Primitive fusion structure, which inherits the advantageous parts of Gyroid and Primitive, possesses a lower Peak Force. For instance, the SEA (Specific Energy Absorption) value increases by 24.4 %, and the CFE (Crush Force Efficiency) increases by 68.5 %. Heteromorphic TPMS with Gyroid and Diamond fusion can bring more flexible designability. Research on Multi-morphology TPMS showed that compared with a single structure, its energy absorption performance was better, and all structures had greatly improved CFE, making them more secure in practical applications. For Multi-morphology TPMS, the MulD&G (A structure that superimposes Diamond and Gyroid) has the highest energy absorption performance, with 76.3 % improvement in CFE compared to the single structure, and the formation of gradient energy absorption in Multi-morphology TPMS depends on the preferential deformation of the inferior structure.