Experiments are conducted on the initial growth of free surface waves on a high-speed (3.5 to 20 m/s) water jet flow that simulates related aspects of the liquid-lithium target in the International Fusion Materials Irradiation Facility. The waves are measured by using laser beam refraction at the water surface. The boundary layer at the nozzle exit and the recovery of the free surface velocity along the jet are also measured. The experimental results confirm that the nozzle-exit boundary layer has a significant influence on the initial growth of waves. With a turbulent boundary layer at the exit, the jet is covered by three-dimensional irregular waves from its beginning. With a laminar boundary layer, however, two-dimensional regular waves grow on an initially smooth water surface. For the latter case, the dominant frequency of the two-dimensional waves agrees well with the linear stability theory of Brennen.