An apparatus and method for measuring a flow velocity profile of fluid traveling in a pipe or conduit uses an ultrasonic wave transmitted from an ultrasonic wave transducer mounted at an angle on the outside of a pipe using a wedge, and made incident onto the fluid in the pipe to measure the fluid flow velocity profile, using the principle that a frequency of an ultrasonic wave, reflected by a reflector existing in the fluid, is changed depending on a flow velocity due to Doppler effect. The transmission frequency and the angle of incidence onto the pipe can be selected to suppress frequency dependence of a measured value due to Lamb wave and allow the flow velocity or flow rate of fluid to be measured with a greater accuracy.