China's economy has undergone remarkable development in the last 20 years. In economic activity, fluctuations are unavoidable, and there are multiple factors that contribute to its volatility, such as earthquakes, and financial crises, etc. At the same time, more and more economists have begun to study the relationship between economic volatility and growth. They use a variety of methods to study volatility, and most of the research case studies are based on data from Western countries. The major subject of this thesis is the investigation of the relationship between Chinese economic volatility and growth. There are 5 indicators which span a period of 20 years (1995~2014) in this thesis: real growth rate, real gross domestic product per capita, gross capital investment share, population growth rate and average schooling. In addition, the dependent variable is real growth rate of real gross domestic product per capita. The data sets used are both provincial level and national level. The ARCH-M model was verified by Engle that it could measure the variance of regression in a valid way. Therefore, the main research object, volatility, will be presented as a conditional variance, and its value will be calculated by Eviews basic on the data of real growth rate. And the ARCH-M model with conditional variance form is the methodology used in this thesis. Thus, the ARCH-LM test will be applied in this thesis in order to examine the ARCH effect on the data. There are three regression equations contained in this thesis: model 1 with s variables, model 2 with 4 variables and, model 3 with conditional variance only. The empirical results obtained in this research show only one conditional variance (Inner Mongolia) from model 3 which presented as statistically significant, and passed the ARCH-LM test. For the other secondary variables, the results are diverse in each province. The short comings of my study, the limited number of observations and variables, causes the provincial empirical results have 8 errors. In addition, there is a high positive correlation between the two variables that result in the regression coefficient which must also refer to the results of the two different models. For the above reasons, we are unable to draw a definite conclusion of the relation between economic growth and volatility. At the end of the paper, some proposals for improvement are presented.