This article proposes and implements a sampling-clockless quasi-digital frequency-key-shifting ( FSK) demodulator with a strong tolerance against carrier-frequency offset. To precisely discriminate periods of the FSK signal without a high-frequency sampling clock, quasi-digital time registers are used to construct pulse-width comparators (PWC) to demodulate the FSK signal, which are robust against the process, voltage, and temperature variation. In addition, a discrete-time differentiator is proposed and integrated into the demodulator to efficiently reject the inevitable carrier frequency offset and drift of the FSK signal. The demodulator is prototyped, analyzed, implemented, and tested. The measurement results show that the demodulator can demodulate FSK signal with a data rate of 1 Mbps and a modulation index of 0. 5, while only requiring a 10. 7 dB signal-to-noise ratio to achieve a demodulation quality with a biterror ratio of no more than 10 -3 while tolerating a frequency offset or drift in the range of -0. 56 to 0. 48 MHz.