This paper proposes an adaptive spectral estimation method for analytic speech signals. The method decreases the calculation errors of finite precision which happen in a method estimating real coefficients. A pre-processing is applied to compensate the discontinuity of a spectrum on decimated analytic signals. Furthermore, the tracking ability of the method estimating complex coefficients is discussed. Its speed is approximately as fast as a conventional method. It is shown from the results of experiments that the proposed method estimates more accurate spectra of speech signals than conventional adaptive methods estimating real coefficients.