Diurnal variation is an important part of the geomagnetic field. In this study, observation data was collected from 2011 to 2013 at three stations (JYG, LZH, and TSY) in the Gansu province. The data focused on time series characteristics of the Hurst exponent of geomagnetic Z-component diurnal variation. The results show that the variation range of the Hurst exponent at JYG and LZH stations is 0.08 and 0.06, respectively. This represents a normal change because the low point is in the middle of a year and the peak point is at the end of the year, completing a change cycle within a year. The change is similar between JYG and LZH stations. In 2012, there was a change in the Hurst exponent exceeding the normal range. On July 22, 2013, the M_S6.6 earthquake occurred at the junction of Minxian and Zhangxian in the Gansu province, 130 km from Tianshui city. The abnormal change of the Hurst exponent at the TSY station may be the result of a magnetic field change induced by the transfer of local, deep thermal mass in the earth. In combination with other research, this may provide an early indication of the Minxian M_S6.6 earthquake. This study provides evidence for further study of the mechanism of geomagnetic diurnal variation anomalies, seismo-magnetic relation, and earthquake prediction.