Abstract: The transition prediction of the hypersonic boundary layer on a flat plate is investigated by using the e^N method under three different wall conditions including the isothermal, adiabatic and wall temperature distribution conditions. The gas parameters are taken as the corresponding air parameters at the height of 30km with the incoming flow Mach numbers 4.5, 6.0 and 7.0. The calculation results are given and analyzed for four different cases of the wall temperature distribution. The initial disturbance amplitude is estimated to be 0.3‰. The transition is assumed to begin when the disturbance amplitude grows up to 1.5%. It can be seen that the transition location is most close to the leading edge in the case of the isothermal wall condition, and the transition location would move forward as the incoming flow Mach number increases. However, it would move backward as the incoming flow Mach number increases under the adiabatic wall condition. In the case of the wall temperature distribution condition, the transition location moves forward as the incoming flow Mach number increases. It is also found that the higher the wall temperature is, the further backward the transition location is (whereas, at Mach number 7.0, the result is different). In the adiabatic wall cases at the incoming flow Mach numbers 4.5 and 6.0, the transition locations are determined by the first mode waves, whereas the transition locations for the other cases are determined by the second mode waves.