A frequency modulation demodulation device and a control method thereof are provided. The frequency modulation demodulation device includes an input terminal, a phase converter, a phase-locked loop circuit, and a frequency offset/shift detector. The phase converter receives an input signal to obtain a phase signal. The phase-locked loop circuit generates a phase adjustment signal according to the phase signal and adjusts the phase signal according to the phase adjustment signal to perform demodulation of the input signal. The phase-locked loop circuit performs signal alignment and signal compensation on the phase signal to generate a filtered phase signal. The phase adjustment signal provides a feedback of and adjusts the phase signal. The frequency offset/shift detector generates a frequency offset/shift determining signal according to the phase adjustment signal. The frequency offset/shift determining signal is related to a phase frequency offset/shift of the input signal.