The Phase-spectrum method (PS), widely used in time delay estimation techniques in the fields of radar and sonar, is applied to detect the wavelength shift for any shape of reflection or transmission spectrum of fiber Bragg grating sensors in homogeneous strain or temperature fields. The peak detection sensitivity to noise is analyzed, and the results show that for single mode FBG sensors, the larger the fiber length and the refractive index is, the more seriously the SNR influences on the peak detection. The experimental results show that compared with conventional algorithms, the proposed method can effectively suppress the random excursion of the central wavelength, and its estimation accuracy is not limited by the wavelength accuracy. Besides, it needs no assumption of the spectrum shapes and no interpolations, and thus reduces the computational consumption. The wavelength detection accuracy is on a scale of pm.