The method of simulating cone lens with spatial light modulator is the most widely used method to generate perfect vortex beams at present. However, the ring width of the generated beam can not be controlled in real time by this method. Here, we propose an approach to generate and control the perfect vortex beams based on computer-generated phase holography in Fourier space. Through theoretical analysis and experimental measurements, We demonstrate that the method presented in this paper enables real-time control of topological charge, radius, and thickness of the generated ring beam by using a coded phase mask. The method offers simple optical path, high beam quality, and simple operation with only one of optical path ajustment. Furthermore, the proposed method can also be used to generate and control other abnormal perfect vortex beams, such as elliptic perfect vortex beams. The experimental results are in good agreement with the theoretical results. Thus, the proposed method based on phase-only computer-generated hologram presents a versatile and simple way of generating and controlling perfect vortex beams.