Velocity measurements, using fiber-optic laser-doppler anemometer, were conducted in steep open-channel flows on smooth and incomplete rough beds. Bed slope was changed from 1/500 to 1/25, which covers Froude number from 0.5 to 3. In this condition, the law of the wall and turbulence intensity distribution were examined. The von Karman constant Kis probed to universal, but the integral constant A decreases as the bed shear stress becomes larger. This decrease of A can be expressed by the decrease of the damping factor B in the van Driest's mixing length distribution in the near-wall region. Turbulence intensity u' normalized by friction velocity U* decreases from the semiempirical universal formula with the increase of the bed shear stress, in the same manner as the velocity distribution.