We measured the superfluid response of dilute 3He–4He solutions confined in a one-dimensional channel of 2.8 nm in diameter using a twofold torsional oscillator. We prepared three 3He concentrations of 0.0, 2.0, and 4.0 at. %, and found that the response of 4.0 at. % decreases by 70 mK at 0.13 MPa from that of liquid 4He. The decrease does not depend strongly on the pressure and is proportional to the 3He concentration. Furthermore, we found the measurement frequency dependence in the same manner as for liquid 4He. The response of 4.0 at. % at a measurement frequency of 0.5 kHz at 0.13 MPa is suppressed by about 40 mK from 2 kHz, and the magnitude of the suppression does not depend strongly on both the 3He concentration and the pressure.