A mode transition from an inductive mode to a helicon mode is observed in a solenoidal inductive discharge immersed in a weak dc magnetic field. The measured electron temperature and the plasma density at the reactor radial boundary show a sudden increase when the magnetic field strength reaches the critical value and the electron cyclotron frequency exceeds the rf driving frequency. These increases are due to the electron heating by the helicon wave. Such increases in the temperature and the density are not observed at the plasma center because the helicon wave cannot propagate to the center of the solenoidal type reactor unless the magnetic field is very high. These results show that the transition of the discharge from the inductive to the helicon mode occurs at the critical magnetic field strength.