It is important to develop a wideband THz absorber for the prevention of terahertz electromagnetic pollution and information leakage. Some commonly used methods, such as metamaterials or dynamic modulation technology, have played important roles in the study of wideband THz absorbers. However, most of these absorbers are rigid or non-stretchable, which limits the practical applications in large mechanical deformation and non-plane scenarios. In the paper, we proposed a stretchable MWCNTs-OH/PDMS composite elastomer using the sugar template method. A series of characterization methods were carried out to verify the excellent compatibility of PDMS and MWCNTs-OH. Benefiting from its hierarchical porous structure, the draw-length ratio of sample and tensile strength reaches ∼ 190% and ∼ 0.4 MPa, respectively. More THz waves could be trapped inside the sample for conductive loss because of better impedance matching and conductivity loss (the smallest square value is ∼0.4 kΩ/□), which leads to wideband and high absorptivity (over 98% in 0.2∼2.0 THz range). Furthermore, the tested value of EMI SE was over 10 dB in 0.22∼1.82 THz frequency range at transmission mode. Combined with inherent hydrophobicity characteristics, the material also could be used in humid and rainy environments. The systemic study of stretchable MWCNTs-OH/PDMS composite elastomer will provide theoretical and technical support for subsequent THz absorption in practical scenarios.