The mechanism of influence of the spin quartets and doublets of d3 ion on the spin-Hamiltonian (SH) parameters(including zero-field splitting(ZFS) and g-factors)of the ground state 4A2(4F) is discussed in terms of complete diagonalization method(CDM) under trigonal symmetry and tetragonal symmetry. And these microcosmic mechanisms, including SO mechanism, SS mechanism, SOO mechanism, SO-SS-SOO combined mechanism have been analyzed. It is found that (1) the contributions to ZFS parameter from the spin quartets and doublets are all important; (2) the contributions to the g-factors of the ground state from the spin quartets are predominant, whereas the contributions from spin doublets are slight. In addition, it is shown that SS mechanism and SOO mechanism are determined by spin quartets in SH parameters calculation.