Two new random polarization smoothing methods using full-aperture elements are proposed on low-coherence lasers, one using birefringent wedge and one using flat birefringent plate. By designing the crystal axis direction and wedge angle of the birefringent plates, the methods can selectively introduce time delay and spatial displacement, so as to obtain fast random evolution of transient polarization by utilizing low spatiotemporal coherence of the laser focal field. Both methods avoid the near field discontinuity and can be used under high fluence. The method using birefringent wedge can slightly improve focal spot uniformity, and the method using flat birefringent plate can obtain non-polarization with DOP lower than 2%. Theoretical studies show that the resulting focal polarization evolves rapidly on sub-picosecond timescales and rapidly covers the entire Poincaré sphere. The method using birefringent wedge is achieved in experiment. The results show that the degree of polarization of the focal spot is reduced from 1 to 0.27, which proves the effectiveness of the full-aperture random polarization smoothing. The full-aperture random polarization smoothing can generate a focal field very close to unpolarized thermal light, which is expected to suppress the laser plasmas instability.