Mesoscale activities over the equatorial Pacific Ocean are dominated by the Rossby and Yanai modes of tropical instability waves (TIWs). The TIW-induced surface velocity has not been accurately estimated in previous diagnostic models, especially for the meridional component across the equator. This study develops a diagnostic model that retains the acceleration terms to estimate the TIW surface velocity from the satellite-observed sea surface height. Validated against moored observations, the velocity across the equator is accurately estimated for the first time, much improved from existing products. The results identify the Rossby- and Yanai-mode TIWs as the northwest–southeastward (NW–SE) velocity oscillations north of the equator and the northeast–southwestward (NE–SW) velocity oscillations on the equator, respectively. Barotropic instability is the dominant energy source of the two TIW modes. The NE–SW velocity oscillation of the Yanai mode is associated with the counterclockwise shear of the South Equatorial Current on the equator. The two TIW modes induce different sea surface temperature patterns and vertical motions. Accurate estimates of TIW velocity are important for studying equatorial ocean dynamics and climate variability in the tropical Pacific Ocean.