We report on the observation of the significant photocurrent response of a carbon nanotube (CNT) heterostructure device illuminated by continuous-wave terahertz (THz) radiation. The device consists of a double-walled CNT macrobundle contacted with two metallic nickel electrodes. A room-temperature current responsivity up to ∼0.3 mA/W was obtained when THz radiation was incident on the position of the CNT/nickel contact. Compared to the results we previously reported for a CNT film/metal heterojunction sample, the device presented here shows improved response performance and a greater potential for THz detection.