A hesitant fuzzy soft set(HFSS) is a combination of the Torra's(2010) hesitant fuzzy set(HFS) and the Molodtsov's(1999) soft set theory. Considering that correlation coefficient is one of the most widely used indices in data analysis, a novel concept of correlation coefficient between HFSSs is proposed. At the same time, the mean and the variance of a HFSS are defined. Based on these concepts, a novel correlation coefficient formulation between two HFSSs is developed. The value of the introduced correlation coefficient between two HFSSs lies in the interval [-1, 1] rather than [0, 1], which is in accordance with the classical correlation coefficient in statistics, thus overcomes the weakness of existing correlation coefficient between HFSSs. The weighted correlation coefficient is also proposed to make it more applicable. Finally, an example of hospital assessment is given to illustrate the applicability and effectiveness of the proposed correlation between HFSSs.