We propose a random polarization smoothing method for low-coherence laser to obtain focal spot with random polarization that evolves rapidly in sub-picosecond timescales. Random polarization smoothing is realized by a half-aperture wave plate with sufficient thickness. The degree of polarization and polarization evolution of the focal spot are studied theoretically. The calculation results show that random polarization smoothing can make the polarization of focal spot evolve rapidly and randomly in time and space. Experimentally, the polarization of the focal spot of low-coherence laser with random polarization smoothing is measured by a single-shot polarimeter. The measurement results show that the degree of polarization of the focal spot is reduced to 0.22 on average, which proves the effectiveness of random polarization smoothing. The random polarization smoothing technique on low-coherence laser is expected to reduce the laser plasmas instability through its multi-dimensional random evolution properties.