We demonstrate the intrinsic memory function of ferroelectric field-effect transistors (FeFETs) based on an integration of individual single-walled carbon nanotubes (SWCNTs) and epitaxial ferroelectric films. In contrast to the previously reported "charge-storage" CNT-FET memories, whose operations are haunted by a lack of control over the "charge traps", the present CNT-FeFETs exhibit a well-defined memory hysteresis loop induced by the reversible remnant polarization of the ferroelectric films. Large memory windows approximately 4 V, data retention time up to 1 week, and ultralow power consumption (energy per bit) of femto-joule, are highlighted in this report. Further simulations and experimental results show that the memory device is valid under operation voltage less than 1 V due to an electric-field enhancement effect induced by the ultrathin SWCNTs.