In this paper, we propose a novel method for detecting the fundamental frequencies of speech signals contaminated by noise. The proposed method exploits an eigen-based subspace principle to estimate unknown parameters of the noisy speech signal. In the proposed method, the estimated parameters are used for recovering the spectrum of the signal buried in noise, and then the restored spectrum is used for pitch extraction. Moreover, the proposed method reduces the computational complexity within the subspace method. In the simulation results, it is shown that the proposed method estimates more accurate fundamental frequencies than the conventional pitch estimation methods with saving the computational complexity.