Taking Linxia Prefecture of Gansu Province as an example, this paper selects the data of tourism development and economic growth from 2001 to 2017, and uses co-integration test, Granger causality test and error correction model to investigate the interaction between development of tourism and economic growth in poverty-stricken areas. The results show that there is a significant positive correlation between tourism development and economic growth in Linxia Prefecture of Gansu Province, and there is a long-term stable equilibrium relationship as well as two-way Granger causality between them. The development of tourism will promote economic growth in Linxia Prefecture of Gansu Province, which will stimulate tourism development in turn. On the basis of this conclusion, the paper puts forward the policy recommendations for vigorously promoting the leap forward development of tourism in Linxia Prefecture of Gansu Province.