Abstract: The phenomena with self-similarity and long-range dependence are widespread in the nature. One of the main approaches that quantificationally measure the long range dependence is to estimate a Hurst exponent, which has been extensively applied in hydrology, climatology, geology, and seismology, etc. Based on the analysis of several popular estimating methods and their virtues and limitations, some common problems in their applications are pointed out, and the corresponding solutions are proposed in this paper. Then, seven methods are used to estimate the Hurst exponent for average monthly temperature anomaly in China from January,1873 to December,1990.To test the effect of the results, mean values are compared with a set of Gaussian distribution random numbers using the randomly shuffling method. The results are as follows: R/S method, Abry-Veitch method, and Whittle method are superior to Variance of residuals, Absolute Value method, Aggregated Variance method, and Periodogram method. The appropriate value of the Hurst exponent is, indicating persistence, i.e., the trend of temperature variations in China in near future will generally be the same as the past. The temperature warming trend from the 1980s indicates another warming trend for hereafter.