Based on continuous gravity data at the Lanzhou and Gaotai seismic stations, variations in continuous gravity prior to the Menyuan earthquake that occurred on January 21, 2016 were analyzed. Fast Fourier transform was used to conduct a power spectral analysis on data sampled five days before and two days after the earthquake. The results showed that the frequency amplitude continuously increased, then decreased to a normal value within one day of the earthquake. Furthermore, data from the second sampling, i.e., data sampled 6 days before the earthquake, was filtered, and we found that the gravity disturbance signal was observed within the 48-h preceding the earthquake, with a period of 4-8 s. The frequency characteristics and gravity disturbance signal observed prior to the Menyuan earthquake may reflect a whole seismogenic process before the earthquake, providing a reference for revealing the mechanism of the Menyuan earthquake.