A revised algorithm of the spectrum moment method for formant frequency estimation is proposed. Second-order and third-order spectrum moments, which reflect the variance and skewness of a spectrum pattern, respectively, are utilized to adjust the frequency regions of centroid calculation. This adjustment improves estimation precision. Experiments using model spectra with an all-pole model gave an estimation error of 1.43 %(male) and 1.07 %(female). Speech material of nineteen kinds of utterances - five Japanese vowels, three kinds of connected vowels and eleven short interrogative sentences - spoken by five male and five female speakers were analyzed. The results gave a mean estimation error of 4.45 % for the male speakers and 7. 30 % for the female speakers.