Near-field polarization distribution of a plasmonic prolate nanospheroid in an incident electromagnetic field versus its polarization and the spheroid's aspect ratio is studied in detail. Polarization of the near-field is described with the help of the 3D generalized Stokes parameters, allowing simple visualization. It is shown that this distribution has a complex structure, which drastically depends on the incident field polarization and parameters of the plasmon resonance of the nanoparticle. Received analytical solutions cover the whole set of particles with shape varying from spherical to the nanoneedles and nanorods by changing the aspect ratio of the spheroid. An experiment for visualization of the vectorial near-field around a plasmonic nanoparticle is proposed.