This study proposes a robust estimation technique for the single-phase grid voltage fundamental frequency under grid disturbances. The technique relies on a demodulation method and a finite-impulse-response-based differentiation filter (DF). A frequency domain analysis for designing the DF is presented and is used to estimate the time-varying fundamental frequency from the instantaneous phase angle obtained by the demodulation method. The technique can reject the negative effects caused by the presence of DC offset and harmonics. The proposed DF shows less sensitivity to the presence of oscillations caused by the demodulation method when compared to a similar finite-impulse-response-based DF. Simulation and experimental results are provided to verify the performance of the proposed technique.