Superfluidity of liquid 4He confined in one-dimensional (1D) nanometer-size channels has been studied by means of a torsional oscillator. When the channel is larger than 2.8 nm in diameter, liquid 4He becomes superfluid at low temperatures and a dissipation due to quantized vortex is observed. The superfluid onset temperature is 1.8 K at 0.14 MPa for the 4.7 nm channel and 0.89 K at 0.01 MPa for the 2.8 nm channel. For the latter, it is suppressed strongly under the application of pressure, and continuously approaches zero at around 2.1 MPa at absolute zero, which suggests a quantum phase transition between the superfluid and nonsuperfluid states in the 1D channel
