High-performance non-volatile memory elements based on carbon-nanotube-enabled vertical field-effect transistors (CN-VFETs) are demonstrated. A thin crosslinking polymer layer, benzocyclobutene (BCB), on top of the gate dielectric acts as the charge storage layer. This results in a large, fully gate sweep programmable, hysteresis in the cyclic transfer curves exhibiting on/off ratios >4 orders of magnitude. The carbon nanotube random network source electrode facilitates charge injection into the charge storage layer, realizing the strong memory effect without sacrificing mobility in the vertical channel. Given their intrinsically simple fabrication and compact size CN-VFETs could provide a path to cost-effective, high-density organic memory devices.