In this paper, the DV-X method of ab-initio calculations and the effective Hamiltonian model are introduced to calculate the crystal-field and spin-orbit parameters of rare earth ions doped in various crystals, especially for the crystal with low-symmetry. For the low-symmetry crystal, the number of parameters is more than that of energy levels, thus experimental energy levels fitting cannot determine all parameters, while ab-initio calculations can determine all crystal-field and spin-orbit parameters accurately. Firstly, the crystal-field and spin-orbit parameters of Yb3+ doped in GdTaO4 crystal are calculated by this model, and then the energy level structure of Yb3+:GdTaO4 is given and the continuous emission band of Yb3+:GdTaO4 emission spectrum is analyzed, which is conducive to the laser tunable and laser mode-locking output, so Yb3+:GdTaO4 is a potential laser medium for high efficiency laser operation and new ultrashort pulse output. Also, the crystal-field and spin-orbit parameters of Yb3+ doped in YTaO4 and ScTaO4 are calculated by this model, and the energy level structures of Yb3+:YTaO4 and Yb3+ :ScTaO4 are given, which leads to a conclusion similar to that drawn from the Yb3+:GdTaO4 crystal.