The sound speed of seawater is not constant. It varies with season, day time, depth and range. This variation was not considered in marine seismic data processing and imaging before deep-water seismic acquisition became a routine activity. As a result, non-ignorable errors may be contained in the final migrated-image of deep-water seismic data. To eliminate such errors, we propose here a scheme for inverting the seawater velocity under the condition that the seabed has a complex topography. In this scheme, the seabed topography is represented by step grids constrained by measured water depth data, and the sound profile is assumed to be the one satisfying the Munk formula. Thus, only the parameters appearing in the Munk formula need to be inverted. This is quite different from the conventional inversion schemes that take the velocity as the inversion target. We use the conjugate gradient method to minimize the objective function given as the sum of squares of traveltime differences. Tests on synthetic common-shot data set show that our scheme presented here works as expected. Applications to real marine data set further validates the reasonability and feasibility of our scheme under complex seabed topography. To investigate the reliability of our inversion scheme, we migrate the real 2D data set using the Kirchhoff migration with the inverted Munk profile as the velocity model. The corresponding results show that the seawater velocity obtained by our inversion scheme improves the imaging quality of underwater structures.