Seismic-data processing flows often ignore spatial and temporal variations in the sea surface during marine seismic acquisition by assuming a flat free surface. However, weather patterns during data acquisition can generate rough sea conditions, which can significantly influence seismic full-wavefield source behavior, including ghost reflections and surface-related multiples, by introducing spatial and temporal distortions of the seismic wavelet. To investigate the effects of rough seas on seismic wave propagation, we have developed and solved a new acoustic wave equation using a mimetic finite-difference time-domain (MFDTD) scheme that uses a dynamic (i.e., moving) generalized coordinate system defined to be conformal to the assumed known time-varying free surface. This “sea-surface” coordinate system allows us to model the full dynamic effects associated with this complex boundary condition. Numerical examples demonstrate that the developed MFDTD method can accurately simulate seismic wavefield propagation on a moving mesh for significant wave heights of 5 m and beyond, and it is thus a reliable tool for applications involving modeling, processing, imaging, and inversion of seismic data acquired in rough seas.