We propose a complex-domain pitch estimation algorithm for narrowband speech signals, which utilizes a complex spectrum containing both amplitude and phase spectrum information. Traditional frequency-domain pitch estimation algorithms assume that a speech signal has a harmonic structure; they estimate a pitch by calculating the distance between the adjacent peaks of the amplitude spectrum corresponding to harmonics. However, only a few peaks can be detected from narrowband speech signals because of their limited bandwidth, resulting in pitch estimation errors. In this article, phase differences between harmonics are utilized as an additional cue for pitch estimation. The phase difference between harmonics refers to the two-step phase difference between successive analysis frames and between the lowest-order harmonic and other harmonics, which is theoretically derived using the pitch. When the phase spectrum for the higher-order harmonic is shifted by the theoretical value, it agrees with the phase spectrum for the lowest-order harmonic. Therefore, for each pitch candidate, the proposed method calculates the shifted phase spectra and combines them with the amplitude spectrum to generate complex spectra. When a pitch candidate is correct, the cumulative sum of the complex spectra is added in the same direction, which emphasizes harmonics even for narrowband speech signals. Results of the objective evaluation show that the proposed method accurately estimates the pitch from narrowband speech signals.