The continuous down-scaling of transistors has been the key to the successful development of current information technology. However, with Moore's law reaching its limits, the development of alternative transistor architectures is urgently needed(1). Transistors require a switching voltage of at least 60 mV for each tenfold increase in current, that is, a subthreshold swing (SS) of 60 mV per decade (dec). Alternative tunnel field-effect transistors (TFETs) are widely studied to achieve a sub-thermionic SS and high I-60 (the current where SS becomes 60 mV dec(-1))(2). Heterojunction (HJ) TFETs show promise for delivering a high I-60, but experimental results do not meet theoretical expectations due to interface problems in the HJs constructed from different materials. Here, we report a natural HJ-TFET with spatially varying layer thickness in black phosphorus without interface problems. We have achieved record-low average SS values over 4-5 dec of current (SSave_4dec 22.9 mV dec(-1) and SSave_5dec 26.0 mV dec(-1)) with record-high I-60 (I-60 = 0.65-1 mu A mu m(-1)), paving the way for application in low-power switches.