A new method of measuring specular X-ray reflectivity curves with a time resolution of milliseconds to seconds is developed. A horizontally convergent X-ray beam having a one-to-one correlation between its direction and energy is realized by a curved crystal or a laterally graded multilayer on an elliptic substrate. The X-ray beam is then incident on the surface of the specimen placed at the focus in such a way that the glancing angle in the vertical direction is the same for all X-ray components, which are reflected in the vertical direction by the surface and diverge in the horizontal plane. The perpendicular momentum transfer continuously changes as a function of the horizontal ray direction since the wavelength change similarly. The normalized linear intensity distribution across the beam direction measured downstream of the specimen represents the X-ray reflectivity curve. Examples of time-resolved measurements of X-ray reflectivity curves are shown.