Linguistic hesitant fuzzy sets (LHFSs) permits the decision maker to apply several linguistic terms with membership degrees to denote his/her preference for one thing. Because this type of fuzzy sets can well reflect the qualitative and quantitative cognition of decision maker and it's uncertainty, it attracts more and more scholarsáttention. Firstly, we put forward the concept of the correlation coefficient of LHFSs, and give the calculation rules and properties of the correlation coefficient and weighted correlation coefficient of LHFSs. The significant characteristic of the introduced correlation coefficient in this paper is that it lies in the interval [-1,1], which is in accordance with the classic correlation coefficient in statistic. However, all the correlation coefficients of LHFSs in other related literature are in the interval [0,1]. Finally, we apply the method proposed in this paper to medical diagnosis, and we compare the results in this paper with the previous research results of the correlation coefficient of LHFSs . As a result, it is found that the distribution of new correlation coefficient of the linguistic hesitant fuzzy sets is better, which can more accurately reflect the relationship between the patients'physical condition and various diseases, so that the diagnosis can be made quickly and efficiently.