The lattice parameters and the local lattice distortions around solute atoms in fcc-Ni solutions were studied using first-principles calculations. The solute atoms considered include Al, Co, Cr, Hf, Mo, Nb, Re, Ru, Ta, Ti, and W. The calculations were performed using supercells with 1 solute atom and 107 solvent atoms. It is found that the atomic size difference, the electronic interactions, and the magnetic spin relations between the solute and solvent atoms all contribute to the lattice distortions. Based on the results from first-principles calculations, the linear composition coefficients of fcc Ni lattice parameter for different solutes were determined, and the lattice parameters of multicomponent Ni-base superalloys as a function of solute composition were predicted. The results are compared with existing experimental measurements, and good agreements are obtained for both the compositional dependence of lattice parameters and the local lattice distortions.