This paper presents a new method for robust fundamental frequency (F0) estimation in the presence of background noise and spectral distortion. We define degree of dominance and a dominance spectrum based on instantaneous frequencies. The degree of dominance allows us to evaluate the magnitude of individual harmonic components of speech signals relative to background noise while eliminating the influence of spectral distortion. The fundamental frequency is robustly estimated from reliable harmonic components easily selected from the dominance spectra. Experiments are performed using white and multi-talker background noise with and without spectral distortion produced by a SRAEN filter. Results show that the present method is better than the commonly-used methods in terms of correct F0 rates.