The deep energy levels and the wavefunctions of V3- in silicon are calculated by using the Koster-Slater Green's function method. Numerical results show that there are five energy levels in the energy gap, i.e., E(A2)=0.417eV, E(B1)=0.492eV, E(B21)=0.512ev, E(A1)=0.532eV, E(B22)=0.608eV. The hyperfine interactions (h.f.) constant associated with these states are calculated. According to the comparison of the theoretical h.f. constant with the experiments, we determine that the B1-state is occupied by the unpaired electron of V3-. The distributed probability of V3- in B1-state on the nearest neighbour atoms is about 60.2%, the major part of which is centered on the two atoms in the plane determined by the trivacancy.