To precisely measure phase signals in phase-sensitive optical time-domain reflectometers, a novel noise-reduction method is proposed that is based on complementary ensemble empirical modal decomposition coupled with singular value decomposition using a permutation entropy algorithm. Initially, a phase signal containing noise is decomposed via complementary ensemble empirical modal decomposition (CEEMD) to obtain a series of components with different frequencies. Subsequently, the PE algorithm is combined with the correlation coefficient mechanism to retain useful components with a larger correlation, and the singular-value-decomposition algorithm is used to denoise the noise components with a smaller correlation. Finally, the useful components, retained after two denoising processes, are reconstructed. Simulation and experimental results demonstrate that, compared with empirical modal decomposition, ensemble empirical modal decomposition, and CEEMD, the proposed method achieves a higher signal-to-noise ratio, which is beneficial for the precise measurement of phase signals.