In both the theoretical and empirical levels, both at home and abroad, the research of the relativity between government debt and economic growth is still inconclusive. Combined with the practical situation of China, this article takes 31 provinces of our country from 1995 to 2014 and 18 (2005, 2013, rejecting) local government debt and economic growth data as samples. First, we conduct unit root test on two variables DEBT and GDP to ensure that data is stationary, and then, on this basis of unit root test, we conduct cointegration test to determine whether there is a long-term cointegration relationship between DEBT and GDP. Finally, on the basis of the first two steps, we conduct Granger causality test on DEBT and GDP. The results show that the local government debt and economic growth in China is the second order sequences that are of single integer. And there may not exist long-term cointegration relationship between DEBT and GDP. In the short term, the economic growth of local government is the Granger cause of local government debt, but the local government debt is not a Granger cause of economic growth of local government. In the medium term, the economic growth of local government is still the Granger cause of local government debt and its performance is more significant. However, local government debt is not the Granger cause of local government economic growth, but it is weaker than the short-term. In the long term, economic growth and government debt of local government exit Reciprocal causation relationship. According to 18 years real data of 31 provinces in China, we design empirical scheme and conduct Granger causality test in using econometric software Eviews 8. This is the possible innovation of this article.