Quantum sensors represent an ideal medium for electromagnetic spectrum detection, offering the potential to overcome the limitations of traditional spectrum measurement principles in response bandwidth and measurement sensitivity, and have broad application prospects. This paper presents an ultra-wideband continuous spectrum measurement system based on Rydberg atoms mixer, and mainly analyzes the impact of local oscillator radio frequency (RF) field on the signal-to-noise ratio (SNR) of beat-note in the non-resonant region. Utilizing atomic non-resonant superheterodyne technology, we realize to measure the electromagnetic wave spectrum with a certain frequency bandwidth on each Rydberg state. By rapid tuning of the local RF field and the coupling laser wavelength, the continuous electromagnetic spectrum measurement across the microwave (1–40 GHz) and terahertz wave(110–170 GHz) bands is realized, achieving a minimum measurable field strength of 0.32 μV/cm in the resonant region and 2.34 μV/cm at 40 GHz in the non-resonant region, with a dynamic range exceeding 70 dB and a frequency resolution less than 10 Hz. This work have verified that quantum sensors based on Rydberg atoms possess the characteristics of full-band and high-sensitivity electromagnetic spectrum response, laying a research foundation for the development of high-sensitivity atomic spectrometers.