During operation of a water turbine, the vibration of its mechanical structure may reflect its operating condition. If the peak value of the vibration displacement exceeds a certain range, the water turbine may malfunction, causing serious accidents resulting in casualties and property damage. Therefore, real-time monitoring of the vibration displacement of water turbines is of great importance to ensure the safe operation of water turbines. Existing vibration displacement calculation methods do not consider the influence of vibration frequency, resulting in significant errors when measuring complex vibration displacements. This paper proposes a grating wavelength conversion method based on Fourier series. First, the wavelength variation of the fiber-optic grating sensor feedback is decomposed into multiple wavelength components containing only a single frequency according to different frequencies. Calculate the vibration acceleration generated by each wavelength component corresponding to the vibration component based on the sensitivity of the sensor. Calculate the vibration displacement generated by each vibration component by quadratic integration of the vibration acceleration. Sum these vibration displacements to obtain the total vibration displacement. Perform displacement measurement for complex vibrations. In order to improve the accuracy of vibration displacement measurement, we conducted calibration experiments on the sensitivity outside the stable operating frequency band of fiber-optic grating sensors, because only a part of the corresponding relationship between vibration frequency and sensitivity is included in the stable operating frequency band. And the corresponding relationship between vibration frequency and wavelength change in this part of the frequency was determined by segmented fitting. Two experiments were designed to compare the ability of this method to calculate vibration displacement with traditional methods. They are the simple harmonic vibration experiment and the complex vibration experiment. The harmonic vibration experiment provides vibration excitation of only a single frequency by a vibration table. In the complex vibration experiment, the vibration excitation generated by the vibration table contains two different vibration frequencies, and there is a certain phase difference between these two different vibration frequencies. The wavelength change of the fiber-optic grating sensor is recorded, and the vibration acceleration and displacement are calculated using the above two methods. In the harmonic vibration experiment, the maximum vibration acceleration error of the traditional method is 4.6%, and the maximum vibration displacement error is 4.6%. The maximum vibration acceleration error of the method in this article is 2.1%, and the maximum vibration displacement error is 3.74%. In complex vibration experiments, the traditional method cannot accurately measure the vibration displacement, and the maximum error of this method is 8.45%. The experimental results of harmonic vibration show that both traditional methods and grating wavelength conversion methods based on Fourier series can accurately measure vibration displacement when there is only a single frequency vibration in the environment. The results of complex vibration experiments show that when there are multiple vibrations of different frequencies in the environment, the grating wavelength conversion method based on Fourier series can accurately decompose and reconstruct the grating wavelength signal, and has higher accuracy and stronger stability in measuring multi-frequency vibration displacement.In addition, we also used these two methods to measure the vibration displacement peak-to-peak values of the stator end and upper frame data of the water turbine, and compared them with the results of the electrical sensors. The experimental results show that the vibration component at the stator end of the water turbine is single, and the vibration displacement peak-to-peak measurement results are similar. The vibration components at the upper frame of the water turbine are complex, and the vibration displacement peak-to-peak measurement results of the traditional method are less than 5 μm. The vibration displacement peak-to-peak measurement results of the electric sensors and the grating wavelength conversion methods based on Fourier series are both around 45 μm. This indicates that the grating wavelength conversion method based on Fourier series has certain practical application value.