In this work, we investigate the generation of optical vortices by means of the so-called radial-phase shift spiral zone plate (RSSZP) from a flat-topped beam (FTB). Based on the process of the extended Huygens-Fresnel integral, an analytical formulation of the field distribution for the generated beam is developed. The evolution of the intensity distribution of the diffracted beam is numerically illustrated by studying the effects of some parameters. Moreover, it is established that the characteristics of the intensity of the generated beam is increased with the beam waist, on the contrary, this intensity is decreased by the augmentation of the beam order N. Furthermore, it is demonstrated that in the case of the topological charge equal to zero. The behavior of the beam is converted into a fundamental Gaussian. However, it is found that, for the topological charge superior to zero we have a vortex beam. In addition, it can be noted that the increase of the beam order leads the dark part size becomes large. In addition, as the shifting parameter is increased, the lobes appear larger. Finally, this research may be useful in different applications such as in optical switches and micromanipulation.