The K^- induced production of Lambda(1405) is investigated in K^- d to pi Sigma n reactions based on coupled-channels chiral dynamics, in order to discuss the resonance position of the Lambda(1405) in the KbarN channel. We find that the K^-d to Lambda(1405)n process favors the production of Lambda(1405) initiated by the KbarN channel. The present approach indicates that the Lambda(1405) resonance position is 1420 MeV rather than 1405 MeV in the pi Sigma invariant mass spectra of K- d to pi Sigma n reactions. This is consistent with an observed spectrum of the K^- d to pi^+ Sigma^- n with 686-844 MeV/c incident K^- by bubble chamber experiments done in the 70s. Our model also reproduces the measured Lambda(1405) production cross section.