Recently, the topological magnetic textures, such as magnetic vortex, skyrmion, meron, have attracted wide attention. Siracusano et al. Siracusano G, Tomasello R, Giordano A, et al. 2016 Phys. Rev. Lett. 117 087204 found a new topological magnetic configuration, named a magnetic radial vortex. The magnetic radial vortex state is a stable topological magnetic texture. The magnetization in the center of the magnetic radial vortex, namely the radial vortex polarity, points upward or downward. The in-plane component of the magnetization, namely, the radial vortex radial chirality, orientates radially outward or inward. The magnetic radial vortex has become another emerging research hotspot after skyrmion, which can be attributed to its better thermal stability and lower driven current density. In this paper, we investigate the nucleation mechanism of magnetic radial vortex under the effect of interfacial Dzyaloshinskii-Moriya interaction (IDMI) by using the micromagnetic simulation. The results indicate that the smaller the diameter of the soft magnetic nanodisk, the more easily the wider range of the intensity of IDMI is created. When the thickness of the disk is increased by one order of magnitude, the magnetic radial vortex can be formed stably. Therefore, the intensity of IDMI can be further reduced by appropriately choosing the disc size. The magnetic radial vortex can be nucleated no matter whether the initial magnetization configuration is circular vortex or uniform state. However, if the initial state is uniform, the magnetization component along the z-axis direction is prerequisite. In the magnetic radial vortex nucleation process, the nucleation time of the uniform state is significantly longer than that of circular vortex, and the energy variation time of circular vortex is longer than that of the uniform state. In the process of the formation of magnetic radial vortex, the variation of magnetic moment, skyrmion number and energy are determined by different initial magnetization configurations. This work contributes to the understanding of the mechanism of magnetic radial vortex and provides a theoretical guideline for choosing reasonable disc size and IDMI strength. Moreover, the above-mentioned conclusions contribute to the practical applications of magnetic radial vortex in spin electric devices.