Wavelet analysis has been carried out to understand the amplification of disturbances appearing prior to the transition to turbulence in a constant-acceleration pipe flow. Air is used as the working fluid and the axial velocity of air flow is measured with a hot-wire anemometer. Transition to turbulence is judged on the basis the histories of the axial velocity, RMS value of the axial velocity fluctuation, and wall shear stress in addition to the result of wavelet analysis. The period from the appearance of disturbances to the onset of turbulence is clarified in relation to the acceleration.