The application of tunnel field-effect transistors (TFETs) in the sub-5.1 nm range meets the challenges of low on-state current (Ion), elevated leakage current (Ileak) and a limited bias range with sub-thermionic subthreshold swing (SS) characteristics. Here, by the design of gate-all-around (GAA) single-chain Te (1Te) TFETs, the sub-thermionic SS characteristics span nearly six orders of magnitude of drain current, overcoming the above challenges. While there usually exists trade-offs between maximizing Ion and minimizing Ileak, our optimized 5.1 nm GAA 1Te TFET defies this convention. Its steep turn-on characteristics result in an ultra-low Ileak of 7.9 × 10−10 μA/μm coupled with a high Ion of 1352 μA/μm, surpassing other low-dimensional materials-based FETs. These exceptional performances are attributed to the desirable properties from ultra-thin 1Te, including its moderate bandgap, anisotropic effective mass, and reduced screening length. Crucially, this device demonstrates key figure of merits for digital electronics that fulfill both the requirements of high-performance and low-power device specified by the International Technology Roadmap for Semiconductors, indicating the potential as energy-efficient and high-speed electronic switch. Our findings are expected to stimulate further research into sub-5.1 nm quasi-1D materials-based TFETs and provide valuable insights for optimizing their performance.