We generate the vector vortex or polarization singular beams using a polarization sensitive spatial light modulator displaying an on-axis hologram of an optical vortex. The generated vector beams are characterized by polarimetry and then scattered through a ground glass plate. The polarimetry for scattered light confirms the presence of random spatial polarization distribution, which is known as polarization speckles, although locally every point is completely polarized. Here, we present the structure and characterization of the generated polarization speckles and their statistical properties.