We propose a quasi-broadband laser scheme to achieve comparable beam smoothing and polarization randomizing performance with the broadband laser in high-power lasers. The quasi-broadband laser can be multi-central frequency and multi-color laser in which each beamlet is a superposition of frequency-modulated lasers with frequency shift, i.e., multi-frequency, and the central wavelengths of the beamlets are different from each other, i.e., multi-color. The quasi-broadband laser can also be multi-color spectrally incoherent laser whose beamlets are from broadband sources with central wavelength shift. In addition, the half-aperture polarization control plate array is applied to randomize the polarization and to enhance the smoothing effect. Results indicate that, the two quasi-broadband laser schemes can generate a rapidly temporally-varying light field with broadened spectrum and degenerated coherence, benefiting the randomization of polarization state and improvement of the irradiation uniformity.