Dynamic tuning of terahertz (THz) wave has a great potential application as smart THz devices, such as switches, modulators, sensors, and so on. However, the realization of flexible THz modulation with high efficiency is rarely observed, which is nearly absent from the booming development and demands on flexible electronics. Here, we report a flexible THz modulation based on conductive polymer composites composed of thermoplastic polyurethane (TPU) and conductive particles (Ni). By designing the additive content of Ni particles, such a flexible layer exhibits resistivity change of 6-7 orders under tensile strain due to the formation of an electron-transport channel provided by the in situ evolution of the Ni network. It could be used to dynamically control the THz transmission with a giant modulation depth of around 96%, at a high strain operation (up to around 58.5%). Moreover, these characteristics are demonstrated to be available for highly tension sensitive THz spectroscopy and imaging. This work opens up a connection between flexible polymer-based composites and THz dynamic devices. It proposes an unprecedented flexible THz modulation with giant tuning efficiency and provides a scheme for contactless and passive tension sensors.