To meet the need to transmit increasingly massive volumes of data, a more than 3 kW continuous wave (CW) Ka-band sheet beam traveling-wave tube (SB-TWT) is reported for the first time. Working under unsaturated drive, the maximum gain obtained is 29 dB with a sheet beam of 30.9 kV, 0.82 A, and the efficiency exceeds 24% with a single-stage collector depressed to −15 kV. The 1-dB bandwidth reaches 6 GHz from 26 GHz to 32 GHz and the bandwidth with output power greater than 2 kW can even reach 7GHz from 26 GHz to 33 GHz. The realization of 99.8% static transmission as well as over 97% actual CW transmission of sheet beam is verified successfully, which benefits from adopting periodic cusp magnet (PCM) focusing, and thereby total weight is less than 15 kg. The relevant experimental details are introduced in this letter.