The illumination uniformity of laser beams in inertial confinement fusion (ICF) facility is a key factor, which plays a crucial role in suppressing the laser plasma instabilities. However, the prevailing beam smoothing techniques cannot meet all the requirements for improving the irradiance uniformity of laser beams and mitigating the laser plasma instabilities, which are determined by the high-frequency spatial modulations and the fine-scale speckles of the focal spots. An ultrafast azimuthal beam smoothing scheme based on vortex beams is proposed in this paper. In this scheme, two of the four beams in a laser quad are transformed from super-Gaussian (SG) beams into vortex beams by inserting two spiral phase plates with opposite topological charges into the beam path, whereas the other two SG beams remain unchanged. By controlling the polarization and the center wavelength of each beam, the SG beam and the transformed vortex beam in the quad are coherently superposed on the target plane, so are the remaining two beams. Owing to the difference in central wavelength and the existence of the topological charges, two focal spots rotating in a period of a few picoseconds are generated in the target plane, which can redistribute the speckles quickly in temporal domain and thus improve the irradiance uniformity of the laser quad. By establishing the physical model of the azimuthal smoothing scheme, the smoothing characteristics including the rotation period, the illumination uniformity and the fractional-power-above-intensity of the focal spots are analyzed in detail. In order to improve the smoothing characteristics significantly, the novel smoothing scheme is further combined with another ultrafast smoothing scheme, i.e. radial smoothing scheme. The influence of the key parameters of the combined smoothing scheme on the illumination uniformity and on the smoothing velocity are discussed. Results indicate that the azimuthal smoothing scheme can achieve the ultrafast smooth of the laser quad in the azimuthal direction and the best illumination uniformity within a few picoseconds as well. Though the degree of improvement in the irradiance uniformity of the azimuthal smoothing scheme is lower than that of the radial smoothing, the combination of these two schemes can improve the uniformity effectively and rapidly. The novel smoothing scheme provides a potential smoothing approach for the high-power laser facilities.