Metasurface antennas (MAs) have been proposed as innovative alternatives to conventional bulky configurations for satellite applications because of their low profile, low cost, and high gain. The general method of surface impedance modulation for designing MAs is complicated, and achieving broad operation bandwidth remains a challenge because of its high dispersion response. We propose a novel and easy technique to control cylindrical surface waves radiated by a phase-tuning metasurface. Simultaneously, this technique exhibits a considerably wide working bandwidth. A detailed analysis of the radiation mechanism is discussed. A left-hand circularly polarized (LHCP) antenna and a right-hand circularly polarized (RHCP) antenna that are based on the phase-tuning metasurface are simulated and measured. The measured fractional 3-dB gain bandwidth and gain are higher than 17% and 15.57 dBi, respectively, which are consistent with the simulated results. Moreover, 30% 3-dB axial ratio is achieved for the LHCP and RHCP antennas. To the best knowledge of the authors, it is for the first time to realize a circularly polarized broadband MA by using the phase-tuning mechanism. The approach can be regarded as a new starting point for antenna design, thereby paving the way for the development of broadband and low-profile antennas for future satellite communication.