We fabricate and measure a single-walled carbon nanotube transistor having a liquid-gate electrode. The ratio value of Ion Ioff is as high as 104, indicating the presence of a semiconducting channel. A passivation layer over the source/drain electrode greatly suppresses the liquid-gate leakage by about three orders of magnitude. The channel currents are noticeably distinct between two liquid samples: distilled water and aqueous solution (1× 10-4 M NaCl). This biological sensing ability is attributed to the different electrical double-layer capacitances with respect to the bulk part of the channel. The corresponding theoretical calculation is carried out in detail.