The 3D seismic data in the prestack domain are contaminated by impulse noise. We have adopted a robust vector median filter (VMF) for attenuating the impulse noise from 3D seismic data cubes. The proposed filter has two attractive features. First, it is robust; the vector median that is the output of the filter not only has a minimum distance to all input data vectors, but it also has a high similarity to the original data vector. Second, it is structure adaptive; the filter is implemented following the local structure of coherent seismic events. The application of the robust and structure-adaptive VMF is demonstrated using an example data set acquired from an area with strong sedimentary rhythmites composed of steep-dipping thin layers. This robust filter significantly improves the signal-to-noise ratio of seismic data while preserving any discontinuity of reflections and maintaining the fidelity of amplitudes, which will facilitate the reservoir characterization that follows.