Detection of the microwave (MW) field with high accuracy is very important in the physical science and engineering fields. Herein, an atomic Rabi resonance-based MW magnetic field sensor with a high-dynamic-range is reported, where α and β Rabi resonances are used to measure MW fields. In MW measurement experiments, the sensor successfully measured a magnetic field of about 10 nT at 9.2 GHz using the α Rabi resonance line on the cesium clock transition and continuously detected the MW magnetic field in the X-band over a high dynamic power range of >60 dB from the β Rabi resonance. Finally, the MW power frequency shift and power broadening are investigated to support more sensitive field measurements. The proposed MW detection method can be extended to cover a higher dynamic range and a wider frequency band by applying stronger excitations and exploring non-clock atomic transitions, respectively. In addition to MW magnetic field sensing, other potential application of the proposed method can be explored, including SI-traceable MW calibration and atomic communication.