Researchers are interested in the sensor based on Rydberg atoms because of its broad testing frequency range and outstanding sensitivity. However, the discrete frequency detection limits its further employment. We expand the frequency range of microwaves using Rydberg atoms under the Zeeman effect. In such a scheme, the magnetic field is employed as a tool to split and modify adjacent Rydberg level intervals to realize tunable frequency measurement over 100 MHz under 0-31.5 Gauss magnetic field. In this frequency range, the microwave has a linear dynamic variation range of 63 dB, and has achieved a sensitivity of 11.72 µV cm-1Hz-1/2 with the minimum detectable field strength of 17.2 µV/cm.. Compared to the no magnetic field scenario, the sensitivity would not decrease. By theoretical analysis, in a strong magnetic field, the tunable frequency range can be much larger than 100 MHz. The proposed method for achieving tunable frequency measurement provides a crucial tool in radars and communication.