We propose an efficient method of generating a vortex beam with multi-foci by using a fractal spiral zone plate (FSZP), which is designed by combining fractal structure with a spiral zone plate (SZP) in the squared radial coordinate. The theoretical analysis reveals that the number of foci that embed vortices is significantly increased as compared with that obtained by using a conventional SZP. Furthermore, the influence of topological charge on the intensity distribution in focal plane is also discussed in detail. For experimental investigation, an FSZP with topological charge p=1 and 6.4 mm diameter is fabricated by using a photo-etching technique. The calibration indicates that the focusing performances of such a kind of zone plane (ZP) accord well with simulations, thereby providing its potential applications in multi-dimensional optical manipulation and optical imaging technology.