This paper proposes a novel robust fundamental frequency (F0) estimation algorithm based on complex-valued speech analysis for an analytic speech signal. Since analytic signal provides spectra only over positive frequencies, spectra can be accurately estimated in low frequencies. Consequently, it is considered that F0 estimation using the residual signal extracted by complex-valued speech analysis can perform better for F0 estimation than that for the residual signal extracted by conventional real-valued LPC analysis. In this paper, the autocorrelation function weighted by AMDF is adopted for the F0 estimation criterion and four signals; speech signal, analytic speech signal, LPC residual and complex LPC residual, are evaluated for the F0 estimation. Speech signals used in the experiments were an IRS filtered speech corrupted by adding white Gaussian noise or Pink noise whose noise levels are 10, 5, 0, -5 [dB]. The experimental results demonstrate that the proposed algorithm based on complex LPC residual can perform better than other methods in noisy environment.