We numerically calculate Luttinger liquid parameter Kin the anisotropic spin XXZD models with spin $s = 1/2$ , 1, and 2. In order to obtain groundstate wavefunctions in Luttinger liquid phases, we employ the $U(1)$ symmetric infinite matrix product states algorithm (iMPS). By using relation between the bipartite quantum fluctuations Fand the so-called finite-entanglement scaling exponents $\kappa$ , the Luttinger liquid parameter Kcan be extracted. For $s = 1/2$ and $D=0$ , the numerically extracted Luttinger liquid parameter Kis shown to be good agreement with the exact value. On using the fact that the spin-1 XXZD Hamiltonian with $ D \leqslant - 2$ can be mapped to an effective spin-1/2 XXZ model, we calculate the Luttinger liquid parameter for the region of $ D \leqslant - 2$ . It is shown that our numerical value of the Luttinger liquid parameter agree well with the exact values, here, the relative error less than $1\%$ . Also, our Luttinger liquid parameter at $\Delta = - 0.5$ and $ D = 0$ is shown to be consistent with the result form the density matrix renormalization group (DMRG) method. These results suggest that the $U(1)$ symmetric iMPS method can be applicable to calculate Luttinger liquid parameters if any system has a $U(1)$ symmetry for gapless phases. For instance, we present our Luttinger liquid parameters for the first time for the spin-1 XXZD model under the other parameters and the spin-2 XXZD model with $D = 1.5$ .