The development of wireless communications is driving the need for compact radiofrequency (RF) devices with up to terahertz (THz) frequency and fabrication processes compatible with that of complementary-metal-oxide-semiconductor (CMOS) transistors. Aligned carbon nanotube (A-CNT) film is a promising candidate semiconductor that can be used to build both CMOS field-effect transistors (FETs) for digital integrated circuits (ICs) and radiofrequency (RF) transistors with frequencies beyond 1 THz for analogue ICs. Herein, we demonstrate the first MOS FET with a cut-off frequency beyond 1 THz on a high-quality A-CNT array film, and with a carrier mobility of 2,000 cm2 V− 1 s− 1 and better scaling characteristics than all semiconductors, including GaAs and InP. The fabricated CNT MOS FETs present a record performance that includes an on-state current of 3.02 mA µm− 1, a peak transconductance of 2.17 mS µm− 1 at a bias of − 1 V, and a saturation velocity of 3.5 × 107 cm s− 1. Through optimising device structure and fabrication process, in particular the introduction of a Y-gate, a 35 nm-gate length A-CNT MOS FET is fabricated that shows extrinsic current-gain/power-gain and cut-off frequencies of up to 551 GHz/1024 GHz, representing the fastest MOS FET for RF applications. Furthermore, CNT-based mmWave band (30 GHz) RF amplifiers are demonstrated with a high gain of 21.4 dB.