Based on the latest high-precision gravity data recorded in Wuhan and global high-accuracy VLBI (very long baseline interferometry) observations, we have determined the intrinsic parameters (including eigen-period and quality factor, et al) of FCN(free core nutation) of Earth's liquid core. Moreover, the viscosity at the top of the liquid core and its real dynamic ellipticity are obtained. By using the Monte Carlo method, we have calculated the uncertainty of the FCN's eigen-period. The results show that the FCN's eigen-periods determined by gravity and VLBI are about 430 sd and the difference between them is 1.47 sd, with the viscosity coefficient of 1 028 Pa·s. This paper discusses the main reasons for the above differences, and finally compares our results with similar research results from China and abroad.