A frequency shift keying demodulator robust for frequency offset is provided. The demodulator is used to enable the signal to be received correctly when the frequency offset occurs. A microprocessor of demodulator controls a frequency mixer and a phase difference generator according to the duty cycle of the preamble when receiving the preamble of the demodulated signal. Therefore, the duty cycle of the preamble of the demodulated signal can be close to 50%, and the data from a transmitter is received correctly.