As an important structured beam, vortex beams have a wide range of applications in many fields. However, conventional vortex beam generators require complex optical systems, and this problem is particularly serious with regards to focused vortex beam generators. The emergence of metasurfaces provides a new idea for solving this problem; however, the accompanying chromatic dispersion limits its practical application. In this paper, we show that the dispersion characteristic of focused vortex beam generators based on metasurfaces can be controlled by simultaneously manipulating the geometric and propagative phases. The simulation results show that the transmission-type focused vortex beam generators exhibit positive dispersion, zero dispersion, and negative dispersion, respectively. This work paves the way for the practical application of focused vortex beam generators.